Maintenance Engineering -- Shaft Alignment

Shaft alignment is the proper positioning of the shaft centerlines of the driver and driven components (i.e., pumps, gearboxes, etc.) that make up the machine drive train. Alignment is accomplished through either shimming or moving a machine component or both. Its objective is to obtain a common axis of rotation at operating equilibrium for two coupled shafts or a train of coupled shafts.

Shafts must be aligned as perfectly as possible to maximize equipment reliability and life, particularly for high-speed equipment. Alignment is important for directly coupled shafts as well as coupled shafts of machines that are separated by distance-even those using flexible couplings. It is important because mis-alignment can introduce a high level of vibration, cause bearings to run hot, and result in the need for frequent repairs. Proper alignment reduces power consumption and noise level and helps to achieve the design life of bearings, seals, and couplings.

Alignment procedures are based on the assumption that one machine-train component is stationary, level, and properly supported by its base plate and foundation. Both angular and offset alignment must be performed in the vertical and horizontal planes, which is accomplished by raising or lowering the other machine components and /or moving them horizontally to align with the rotational centerline of the stationary shaft. The movable components are designated as machines to be moved (MTBM) or machines to be shimmed (MTBS). MTBM generally refers to corrections in the horizontal plane, while MTBS generally refers to corrections in the vertical plane.

Too often, alignment operations are performed randomly, and adjustments are made by trial and error, resulting in a time-consuming procedure. Because of this problem, Integrated Systems, Inc. (ISI) developed this module to help maintenance technicians speed up the alignment process. It presents a step-by-step procedure for the proper alignment of machinery and discusses shaft alignment fundamentals, equipment, measurements, and computations. Because there are certain basic math skills needed to perform alignment computations, a math review also is included.


This section discusses the basic fundamentals of machine alignment and presents an alternative to the commonly used method, trial and error. This section addresses exactly what alignment is and the tools needed to perform it, why it's needed, how often it should be performed, what is considered to be ''good enough,'' and what steps should be taken prior to performing the alignment procedure. It also discusses types of alignment (or misalignment), alignment planes, and why alignment is performed on shafts as opposed to couplings.

Shafts are considered to be in alignment when they are colinear at the coupling point. The term colinear refers to the condition when the rotational centerlines of two mating shafts are parallel and intersect (i.e., join to form one line). When this is the case, the coupled shafts operate just like a solid shaft. Any deviation from the aligned or colinear condition, however, results in abnormal wear of machine-train components such as bearings and shaft seals.

Variations in machine-component configuration and thermal growth can cause mounting-foot elevations and the horizontal orientations of individual drive-train components to be in different planes. Nevertheless, they are considered to be properly aligned as long as their shafts are colinear at the coupling point.

Note that it's important for final drive-train alignment to compensate for actual operating conditions because machines often move after start-up. Such movement is generally the result of wear, thermal growth, dynamic loads, and support or structural shifts. These factors must be considered and compensated for during the alignment process.

Tools most commonly used for alignment procedures are dial indicators, adjust-able parallels, taper gauges, feeler gauges, small-hole gauges, and outside micrometer calipers.


Periodic alignment checks on all coupled machinery are considered to be one of the best ''tools'' in a preventive maintenance program. Such checks are important because the vibration effects of misalignment can seriously damage a piece of equipment. Misalignment of more than a few thousandths of an inch can cause vibration that significantly reduces equipment life.

Although the machinery may have been properly aligned during installation or during a previous check, misalignment may develop over a very short period of time. Potential causes include foundation movement or settling, accidentally bumping the machine with another piece of equipment, thermal expansion, distortion caused by connected piping, loosened hold-down nuts, expanded grout, rusting of shims, etc.

Indications of misalignment in rotating machinery are shaft wobbling, excessive vibration (in both radial and axial directions), excessive bearing temperature (even if adequate lubrication is present), noise, bearing wear pattern, and coupling wear.


Many alignments are done by the trial-and-error method. Although this method may eventually produce the correct answers, it's extremely time-consuming and , as a result, it's usually considered ''good enough'' before it really is. Rather than relying on ''feel'' as with trial-and-error, some simple trigonometric principles allow alignment to be done properly with the exact amount of correction needed, either measured or calculated, taking the guesswork out of the process. Such accurate measurements and calculations make it possible to align a piece of machinery on the first attempt.


This is a difficult question to answer, because there are vast differences in machinery strength, speed of rotation, type of coupling, etc. It also is important to understand that flexible couplings don't cure misalignment problems-a common myth in industry. Although they may somewhat dampen the effects, flexible couplings are not a total solution.

An easy (perhaps too easy) answer to the question of what is good enough is to align all machinery to comply exactly with the manufacturers' specifications.

However, the question of which manufacturers' specifications to follow must be answered, as few manufacturers build entire assemblies. Therefore an alignment is not considered good enough until it's well within all manufacturers' tolerances and a vibration analysis of the machinery in operation shows the vibration effects caused by misalignment to be within the manufacturers' specifications or accepted industry standards. Note that manufacturers' alignment specifications may include intentional misalignment during ''cold'' alignment to compensate for thermal growth, gear lash, etc. during operation.


If all couplings were perfectly bored through their exact center and perfectly machined about their rim and face, it might be possible to align a piece of machinery simply by aligning the two coupling halves. However, coupling eccentricity often results in coupling misalignment. This does not mean, however, that dial indicators should not be placed on the coupling halves to obtain alignment measurements. It does mean that the two shafts should be rotated simultaneously when obtaining readings, which makes the couplings an extension of the shaft centerlines whose irregularities will not affect the readings.

Although alignment operations are performed on coupling surfaces because they are convenient to use, it's extremely important that these surfaces and the shaft ''run true.'' If there is any runout (i.e., axial or radial looseness) of the shaft and /or the coupling, a proportionate error in alignment will result. Therefore, prior to making alignment measurements, the shaft and coupling should be checked and corrected for runout.


There are four alignment conditions: perfect alignment, offset or parallel mis-alignment, angular or face misalignment, and skewed or combination misalignment (i.e., both offset and angular).

ill. 7.1 Perfect alignment.


Two perfectly aligned shafts are colinear and operate as a solid shaft when coupled. This condition is illustrated in ill. 7.1. However, it's extremely rare for two shafts to be perfectly aligned without an alignment procedure being performed on them. In addition, the state of alignment should be monitored on a regular basis to maintain the condition of perfect alignment.


Offset misalignment, also referred to as parallel misalignmen t, refers to the distance between two shaft centerlines and is generally measured in thousandths of an inch. Offset can be present in either the vertical or horizontal plane. ill. 7.2 illustrates offset, showing two mating shafts that are parallel to each other but not colinear. Theoretically, offset is measured at the coupling centerline.


A sound knowledge of angular alignment, also called face misalignmen t, is needed for understanding alignment conditions and performing the tasks associated with machine-train alignment, such as drawing alignment graphics, calculating foot corrections, specifying thermal growth, obtaining target specifications, and determining spacer-shaft alignment.

Angular misalignment refers to the condition when the shafts are not parallel but are in the same plane with no offset. This is illustrated in ill. 7.3. Note that with angular misalignment, it's possible for the mating shafts to be in the same plane at the coupling-face intersection but to have an angular relationship such that they are not colinear.

ill. 7.2 Offset misalignment.

ill. 7.3 Angular misalignment (no offset).

Angularity is the angle between the two shaft centerlines, which generally is expressed as a ''slope,'' or ''rise over run,'' of so many thousandths of an inch per inch (i.e., unitless) rather than as an angle in degrees. It must be determined in both the vertical and horizontal planes. ill. 7.4 illustrates the angles involved in angular misalignment.

From a practical standpoint, it's often difficult or undesirable to position the stems of the dial indicators at 90-degree angles to the rim and /or face surfaces of the coupling halves. For this reason, brackets are used to mount the devices on the shaft or a non-movable part of the coupling to facilitate taking readings and to ensure greater accuracy. This is a valid method because any object that's securely attached and rotated with the shaft or coupling hub becomes a radial extension of the shaft centerline and can be considered an integral part of the shaft. However, this somewhat complicates the process and requires right-triangle concepts to be understood and other adjustments (e.g., indicator sag) to be made to the readings.

Compare the two diagrams in ill. 7.5. ill. 7.5a is a common right triangle and ill. 7.5b is a simplified view of an alignment-measuring apparatus, or fixture, that incorporates a right triangle.

ill. 7.4 Angles are equal at the coupling or shaft centerline.

ill. 7.5 Common right triangle and simplified alignment-measuring apparatus. The length of side ''b'' is measured with a tape measure and the length of side ''a'' is measured with a device such as a dial indicator. Note that this diagram assumes the coupling is centered on the shaft and that its centerline is the same as the shaft's. Angle ''A'' in degrees is calculated by

A = ta n^-1› 1 a/b

This formula yields the angle ''A'' expressed in degrees, which requires the use of a trigonometric table or a calculator that's capable of determining the inverse tangent. Although technically correct, alignment calculations don't require the use of an angle value in degrees. Note that it's common industry practice to refer to the following value as ''Angle-A,'' even though it's not truly an angle and is actually the tangent of Angle ''A'':

'' Angle-A'' = a/b = rise/run

Figures 7.6 and 7.7 illustrate the concept of rise and run. If one assumes that line O-A in ill. 7.6 represents a true, or target, shaft centerline, then side ''a'' of the triangle represents the amount of offset present in the actual shaft, which is referred to as the rise.

(Note that this ''offset'' value is not the true theoretical offset as defined in Section 2. It is actually the theoretical offset plus one-half of the shaft diameter (see ill. 7.5), because the indicator dial is mounted on the outside edge of the shaft as opposed to the centerline. However, for the purposes of alignment calculations, it's not necessary to use the theoretical offset or the theoretical run that corresponds to it. ill. 7.7 illustrates why this is not necessary.) ill. 7.7 illustrates several rise/run measurements for a constant ''Angle-A.'' Unless ''Angle-A'' changes, an increase in rise results in a proportionate increase in run. This relationship allows the alignment calculations to be made without using the theoretical offset value and its corresponding run.

ill. 7.6 Concept of rise and run.

ill. 7.7 Ris e// run measurements for constant angle.

Therefore, the calculation of ''Angle-A'' can be made with any of the rise/run measurements:

''Angl e-A'' = ris e1

ru 1= ris e2

run2 = ris e3

run3 = ris e4


For example, if the rise at a machine foot is equal to 0.5 inches with a run of 12 inches, ''Angle-A'' is '' Angl e-A'' = 0 5

1 2 0 00 =

0 042 If the other machine foot is 12 inches away (i.e., run = 24 inches), the following relationship applies:

0 042 = X 2 4 0 00 where X or rise = 1 inch


Combination or skewed misalignment occurs when the shafts are not parallel (i.e., angular) nor do they intersect at the coupling (i.e., offset). ill. 7.8 shows two shafts that are skewed, which is the most common type of misalignment problem encountered. This type of misalignment can occur in either the horizontal or vertical plane, or in both the horizontal and vertical planes.

For comparison, see ill. 7.3, which shows two shafts that have angular misalignment but are not offset. ill. 7.9 shows how an offset measurement for non-parallel shafts can vary depending on where the distance between two shaft centerlines is measured. Again, note that theoretical offset is defined at the coupling face.

ill. 7.8 Offset and angular misalignment.

ill. 7.9 Offset measurement for angularly misaligned shafts.


There are two misalignment planes to correct: vertical and horizontal. Therefore, in the case in which at least two machines make up a machine-train, four types of misalignment can occur: vertical offset, vertical angularity, horizontal offset, and horizontal angularity. These can occur in any combination, and in many cases, all four are present.


Both angular misalignment and offset can occur in the vertical plane. Vertical misalignment, which is corrected by the use of shims, is usually illustrated in a side-view drawing as shown in ill. 7.10.


Both offset and angular misalignment can occur in the horizontal plane. Shims are not used to correct for horizontal misalignment, which is typically illustrated in a top-view drawing as shown in ill. 7.11. This type of misalignment is corrected by physically moving the MTBM.

ill. 7.10 Vertical misalignment. STATIONARY; MTBM (MACHINE TO BE MOVED)

ill. 7.11 Horizontal misalignment.


It is crucial that alignment procedures be performed correctly, regardless of what method from Section 3 is used. Actions to be taken before alignment are discussed in the following sections, which cover the preparatory steps as well as two major issues (i.e., soft-foot and indicator sag corrections) that must be resolved before alignment can be accomplished. This section provides procedures for making these corrections as well as the proper way to tighten hold-down nuts, an important procedure needed when correcting soft-foot.

Preparatory Steps

The following preparatory steps should be taken before attempting to align a machine train:

1. Before placing a machine on its base, make sure that both the base and the bottom of the machine are clean, rust free, and don't have any burrs. Use a wire brush or file on these areas if necessary.

2. Common practice is to position, level, and secure the driven unit at the required elevation prior to adjusting the driver to align with it. Set the driven unit's shaft centerline slightly higher than the driver.

3. Make all connections, such as pipe connections to a pump or output shaft connections on a reducer, to the driven unit.

4. Use only clean shims that have not been ''kinked'' or that don't have burrs.

5. Make sure the shaft does not have an indicated runout.

6. Before starting the alignment procedure, check for ''soft-foot'' and correct the condition.

7. Always use the correct tightening sequence procedure on the hold-down nuts.

8. Determine the amount of indicator sag before starting the alignment procedure

9. Always position the stem of the dial indicator so that it's perpendicular to the surface against which it will rest. Erroneous readings will result if the stem is not placed at a 90-degree angle to the surface.

10. Avoid lifting the machine more than is absolutely necessary to add or remove shims.

11. Jacking bolt assemblies should be welded onto the bases of all large machinery. If they are not provided, add them before starting the alignment procedure. Use jacking bolts to adjust for horizontal offset and angular misalignment and to hold the machine in place while shimming.


Soft-foot is the condition when all four of a machine's feet don't support the weight of the machine. It is important to determine if this condition is present prior to performing shaft alignment on a piece of machinery. Not correcting soft-foot prior to alignment is a major cause of frustration and lost time during the aligning procedure.

The basis for understanding and correcting soft-foot and its causes is the know-ledge that three points determine a plane. As an example, consider a chair with one short leg. The chair will never be stable unless the other three legs are shortened or the short leg is shimmed. In this example, the level floor is the ''plane'' and the bottom tips of the legs are the ''points'' of the plane. Three of the four chair tips will always rest on the floor. If a person is sitting with his or her weight positioned above the short leg, it will be on the floor and the normal leg diagonally opposite the short leg will be off the floor.

As in the chair example, when a machine with soft-foot is placed on its base, it will rest on three of its support feet unless the base and the bottoms of all of the feet are perfectly machined. Further, because the feet of the machine are actually square pads and not true points, it's possible that the machine can rest on two support feet, ones that are diagonally opposite each other. In this case, the machine has two soft-feet.


Possible sources of soft-foot are shown in ill. 7.12.

ill. 7.12 Diagrams of possible soft-foot causes. 1, Loose foot. 2, Cocked foot. 3, Bad shim. 4, Debris under foot. 5, Irregular base surface. 6, Cocked foot.


Placing a piece of machinery in service with uncorrected soft-foot may result in the following:

Dial-indicator readings taken as part of the alignment procedure can be different each time the hold-down nuts are tightened, loosened, and retightened. This can be extremely frustrating because each attempted correction can cause a soft-foot condition in another location.

The nuts securing the feet to the base may loosen, resulting in either machine looseness and /or misalignment. Either of these conditions can cause vibration, which can be dangerous to personnel as well as to the machine.

If the nuts don't loosen, metal fatigue may occur at the source of soft-foot.

Cracks can develop in the support base/frame and , in extreme cases, the soft-foot may actually break off.

Initial Soft-foot Correction

The following steps should be taken to check for and correct soft-foot:

Before setting the machine in place, remove all dirt, rust, and burrs from the bottom of the machine's feet, the shims to be used for leveling, and the base at the areas where the machine's feet will rest.

Set the machine in place, but don't tighten the hold-down nuts.

Attempt to pass a thin feeler gauge underneath each of the four feet.

Any foot that's not solidly resting on the base is a soft-foot. (A foot is considered ''soft'' if the feeler gauge passes beneath most of it and only contacts a small point or one edge.) If the feeler gauge passes beneath a foot, install the necessary shims beneath that foot to make the ''initial'' soft-foot correction.

Final Soft-foot Correction

The following procedure describes the final soft-foot correction:

Tighten all hold-down nuts on both the stationary machine and the MTBS.

Secure a dial-indicator holder to the base of the stationary machine and the MTBS. The stem of the dial indicator should be in a vertical position above the foot to be checked. A magnetic-base indicator holder is most suitable for this purpose.

Set the dial indicator to zero. Completely loosen the hold-down nut on the foot to be checked. Watch the dial indicator closely for foot movement during the loosening process.

If the foot rises from the base when the hold-down nut is loosened, place beneath the foot an amount of shim stock equal to the amount of deflection shown on the dial indicator.

Retighten the hold-down nut and repeat the entire process once again to ensure that no movement occurs.

Move the dial indicator and holder to the next foot to be checked and repeat the process. Note: The nuts on all of the other feet must remain securely tightened when a foot is being checked for a soft-foot condition.

Repeat the above process on all of the feet.

Make a three-point check on each foot by placing a feeler gauge under each of the three exposed sides of the foot. This determines if the base of the foot is cocked.

Tightening Hold-Down Nuts

Once soft-foot is removed, it's important to use the correct tightening procedure for the hold-down nuts. This helps ensure that any unequal stresses that cause the machine to shift during the tightening procedure remain the same throughout the entire alignment process. The following procedure should be followed:

After eliminating soft-foot, loosen all hold-down nuts.

Number each machine foot in the sequence in which the hold-down nuts will be tightened during the alignment procedure. The numbers (1, 2, 3, and 4) should be permanently marked on, or near, the feet.

It is generally considered a good idea to tighten the nuts in an ''X'' pattern as illustrated in ill. 7.13.

Always tighten the nuts in the sequence in which the positions are numbered (1, 2, 3, and 4).

Loosen nuts in the opposite sequences (4, 3, 2, and 1).

Use a torque wrench to tighten all nuts with the same amount of torque.

A similar procedure should be used for base plates.

Always tighten the nuts as though the final adjustment has been made, even if the first set of readings has not been taken.

ill. 7.13 Correct bolting sequence for tightening nuts.


Indicator sag is the term used to describe the bending of the mounting hardware as the dial indicator is rotated from the top position to the bottom position during the alignment procedure. Bending can cause significant errors in the indicator readings that are used to determine vertical misalignment, especially in rim-and-face readings (see Section 3). The degree to which the mounting hardware bends depends on the length and material strength of the hardware.

To ensure that correct readings are obtained with the alignment apparatus, it's necessary to determine the amount of indicator sag present in the equipment and to correct the bottom or 6 o'clock readings before starting the alignment process.

Dial indicator mounting hardware consists of a bracket clamped to the shaft, which supports a rod extending beyond the coupling. When two shafts are perfectly aligned, the mounting rod should be parallel to the axis of rotation of the shafts. However, the rod bends or sags by an amount usually measured in mils (thousandths of an inch) because of the combined weight of the rod and the dial indicator attached to the end of the rod. ill. 7.14 illustrates this problem.

Indicator sag is best determined by mounting the dial indicator on a piece of straight pipe of the same length as in the actual application. Zero the dial indicator at the 12 o'clock , or upright, position and then rotate 180 degrees to the 6 o'clock position. The reading obtained, which will be a negative number, is the measure of the mounting-bracket indicator sag for 180 degrees of rotation and is called the sag facto r. All bottom or 6 o'clock readings should be corrected by subtracting the sag factor.

ill. 7.14 Dial indicator sag.

Example 1: Assume that the sag factor is 0.006 inch. If the indicator reading at 6 o'clock equals + 0.010 inch, then the true reading is:

Indicator reading sag factor (+ 0 01 0 ) ( 0 00 6 ) = + 0 01 6

Example 2: If the indicator reading at 6 o'clock equals 0 010 inch, then the true reading is: ( 0 01 0 ) ( 0 00 6 ) = 0 00 4

As shown by the above examples, the correct use of positive (+) and negative (-) signs is important in shaft alignment.


There are two primary methods of aligning machine-trains: dial-indicator alignment and optical, or laser, alignment. This section provides an overview of each, with an emphasis on dial-indicator methods.

Dial-indicator methods (i.e., reverse dial indicator and the two variations of the rim-and-face method) use the same type of dial indicators and mounting equipment.

However, the number of indicators and their orientations on the shaft are different. The optical technique does not use this device to make measurements but uses laser transmitters and sensors.

While the dial-indicator and optical methods differ in the equipment and /or equipment setup used to align machine components, the theory on which they are based is essentially identical. Each method measures the offset and angularity of the shafts of movable components in reference to a preselected stationary component. Each assumes that the stationary unit is properly installed and that good mounting, shimming, and bolting techniques are used on all machine components.

Dial-indicator Methods

There are three methods of aligning machinery with dial indicators.

These methods are (1) the two-indicator method with readings taken at the stationary machine; (2) the two-indicator method with readings taken at the machine to be shimmed; and (3) the indicator reverse method. Methods 1 and 2 are often considered to be one method, which is referred to as rim-and fac e.

Method Selection

Although some manufacturers insist on the use of the indicator reverse method for alignment or at least as a final check of the alignment, two basic factors determine which method should be used. The determining factors in method selection are (1) end play and (2) distance versus radius.

End Play or Float: Practically all machines with journal or sleeve bearings have some end play or float. It is considered to be manageable if sufficient pressure can be applied to the end of the shaft during rotation to keep it firmly seated against the thrust bearing or plate. However, for large machinery or machinery that must be energized and ''bumped'' to obtain the desired rotation, application of pressure on the shaft is often difficult and /or dangerous. In these cases, float makes it impossible to obtain accurate face readings; therefore, the indicator reverse method must be used as float has a negligible effect.

Distance Versus Radius : If float is manageable, then there is a choice of which of the methods to use. When there is a choice, the best method is determined by the following rule:

If the distance between the points of contact of the two dial indicators set up to take rim readings for the indicator reverse method is larger than one half the diameter of travel of the dial indicator set up to take face readings for the two-indicator method, the indicator reverse method should be used.

This rule is based on the fact that misalignment is more apparent (i.e., dial indicator reading will be larger) under these circumstances, and therefore corrections will be more accurate.


Dial indicators and mounting hardware are the equipment needed to take alignment readings.

Dial Indicators: ill. 7.15 shows a common dial indicator, which is also called a runout gaug e. A dial indicator is an instrument with either jeweled or plain bearings, precisely finished gears, pinions, and other precision parts designed to produce accurate measurements. It is possible to take measurements ranging from one-thousandth (0.001 inch or one mil) to 50 millionths of an inch.

The point that contacts the shaft is attached to a spindle and rack. When it encounters an irregularity, it moves. This movement is transmitted to a pinion, through a series of gears, and on to a hand or pointer that sweeps the dial of the indicator. It yields measurements in (+) or (-) mils.

Measurements taken with this device are based on a point of reference at the ''zero position,'' which is defined as the alignment fixture at the top of the shaft- referred to as the 12 o'clock position. To perform the alignment procedure, readings also are required at the 3, 6, and 9 o'clock positions.

ill. 7.15 Common dial indicator. It is important to understand that the readings taken with this device are all relative, meaning they are dependent on the location at which they are taken.

Rim readings are obtained as the shafts are rotated and the dial indicator stem contacts the shaft at a 90-degree angle. Face readings, which are used to deter-mine angular misalignment, are obtained as the shafts are rotated and the stem is parallel to the shaft centerline and touching the face of the coupling.

Mounting Hardware : Mounting hardware consists of the brackets, posts, connectors, and other hardware used to attach a dial indicator to a piece of machinery. Dial indicators can easily be attached to brackets and , because brackets are adjustable, they can easily be mounted on shafts or coupling hubs of varying size. Brackets eliminate the need to disassemble flexible couplings when checking alignments during predictive maintenance checks or when doing an actual alignment. This also allows more accurate ''hot alignment'' checks to be made.

The brackets are designed so that dial indicators can easily be mounted for taking rim readings on the movable machine and the fixed machine at the same time. This facilitates the use of the indicator reverse method of alignment.

If there is not enough room on the shafts, it's permissible to attach brackets to the coupling hubs or any part of the coupling that's solidly attached to the shaft.

Do not attach brackets to a movable part of the coupling, such as the shroud.

Note that misuse of equipment can result in costly mistakes. One example is the improper use of magnetic bases, which are generally designed for stationary service. They are not designed for direct attachment to a shaft or coupling that must be rotated to obtain the alignment readings. The shift in forces during rotation can cause movement of the magnetic base and erroneous readings.

Methods : There are three primary methods of aligning machine-trains with dial indicators: reverse-dial indicator method, also called indicator-reverse method, and two variations of the rim-and-face method.

With all three of these methods, it's usually possible to attach two dial indicators to the machinery in such a manner that both sets of readings can be taken simultaneously. However, if only one indicator can be attached, it's acceptable to take one set of readings, change the mounting arrangement, and then take the other set of readings.

There are advantages with the reverse-dial indicator method over the rim-and-face method-namely, accuracy, and the fact that the mechanic is forced to perform the procedure ''by the book'' as opposed to being able to use ''trial and error.'' Accuracy is much better because only rim readings are used. This is because rim readings are not affected by shaft float or end play as are face readings. In addition, the accuracy is improved as compared with rim-and-face methods because of the length of the span between indicators.

Reverse-dial Indicator Reverse-dial indicator method (also referred to as indicator reverse method) is the most accurate form of mechanical alignment. This technique measures offset at two points, and the amount of horizontal and vertical correction for offset and angularity is calculated. Rim readings are taken simultaneously at each of the four positions (12, 3, 6, and 9 o'clock ) for the movable machine (MTBS/MTBM) and the stationary machine. The measuring device for this type of alignment is a dual-dial indicator, and the most common configuration is that shown in ill. 7.16.

Mounting Configuration and Readings

Dual runout gauges are rigidly mounted on special fixtures attached to the two mating shafts. The runout gauges are mounted so that readings can be obtained for both shafts with one 360-degree rotation.

When the reverse-dial fixture is mounted on mating shafts, the dials initially should be adjusted to their zero point. Once the dials are zeroed, slowly rotate the shafts in 90-degree increments. Record runout readings from both gauges, being sure to record the positive or negative sign, when the fixture is at the 12, 3, 6, and 9 o'clock positions.

ill. 7.16 Typical reverse-dial indicator fixture and mounting.


There are potential errors or problems that limit the accuracy of this alignment technique. The common ones include data recording errors, failure to correct for indicator sag, mechanical looseness in the fixture installation, and failure to properly zero and /or calibrate the dial indicator.

Data Recording : One of the most common errors made with this technique is reversing the 3 and 9 o'clock readings. Technicians have a tendency to reverse their orientation to the machine-train during the alignment process. As a result, they often reverse the orientation of the recorded data.

To eliminate this problem, always acquire and record runout readings facing away from the stationary machine component. In this orientation, the 3 o'clock data are taken with the fixture oriented at 90 degrees (horizontal) to the right of the shafts. The 9 o'clock position is then horizontal to the left of the shafts.

Indicator Sag : The reverse dial indicator fixture is composed of two mounting blocks, which are rigidly fixed to each of the mating shafts. The runout gauges, or dial indicators, are mounted on long, relatively small-diameter rods, which are held by the mounting blocks. As a result of this configuration, there is always some degree of sag or deflection in the fixtures. See Section 2 for a discussion on measuring and compensating for indicator sag.

Mechanical Looseness : As with all measurement instrumentation, proper mounting techniques must be followed. Any looseness in the fixture mounting or at any point within the fixture will result in errors in the alignment readings.

Zeroing and Calibrating : It is very important that the indicator dials be properly zeroed and calibrated before use. Zeroing is performed once the fixture is mounted on the equipment to be aligned at the 12 o'clock position. It is accomplished either by turning a knob located on the dial body or by rotating the dial face itself until the dial reads zero. Calibration is performed in the instrument lab by measuring known misalignments. It is important for indicator devices to be calibrated before each use.

Rim-and-face: There are two variations of the rim-and-face method. One requires one rim reading and one face reading at the stationary machine, where the dial indicator mounting brackets and posts are attached to the machine to be shimmed. The other method is identical, except that the rim and face readings are taken at the machine to be shimmed, where the dial indicator mounting brackets and posts are attached to the stationary machine.

As with the reverse-dial indicator method, the measuring device used for rim-and face alignment is also a dial indicator. The fixture has two runout indicators mounted on a common arm as opposed to reverse-dial fixtures, which have two runout indicators mounted on two separate arms.

The rim-and-face gauges measure both the offset and angularity for the movable machine train component only (as compared with the reverse-dial method, which measures offset and calculates angularity for both the stationary and movable components). With the rim-and-face method, one dial indicator is mounted perpendicular to the shaft, which defines the offset of the movable shaft. The second indicator is mounted parallel to the shaft, which registers the angularity of the movable shaft. ill. 7.17 illustrates the typical configuration of a rim-and face fixture.

Mounting: As with the reverse-dial alignment fixture, proper mounting of the rim-and-face fixture is essential. The fixture must be rigidly mounted on both the stationary and movable shafts. All mechanical linkages must be tight and looseness held to an absolute minimum. Any fixture movement will distort both the offset and angularity readings as the shafts are rotated through 360 degrees.

Rim-and-face measurements are made in exactly the same manner as those of reverse-dial indicator methods. The shafts are slowly rotated in a clockwise direction in 90-degree increments. Measurements, including positive and negative signs, should be recorded at the 12, 3, 6, and 9 o'clock positions.

Limitations: Rim-and-face alignment is subject to the same errors as those of the reverse-dial indicator system, which are discussed in Section 3. As with that system, care must be taken to ensure proper orientation with the equipment and accurate recording of the data.

Note that rim-and-face alignment can't be used when there is any end play, or axial movement, in the shafts of either the stationary or movable machine-train components. Since the dial indicator that's mounted parallel to the shaft is used to measure the angularity of the shafts, any axial movement or ''float'' in either shaft will distort the measurement.

ill. 7.17 Typical configuration of a rim-and-face fixture.


Optical or laser alignment systems are based on the same principles as the reverse-dial method but replace the mechanical components such as runout gauges and cantilevered mounting arms with an optical device such as a laser.

As with the reverse-dial method, offset is measured and angularity is calculated.

A typical system, which is shown in ill. 7.18, uses two transmitter/sensors rigidly mounted on fixtures similar to the reverse-dial apparatus. When the shaft is rotated to one of the positions of interest (i.e., 12 o'clock , 3 o'clock , etc.), the transmitter projects a laser beam across the coupling. The receiver unit detects the beam, and the offset and angularity are determined and recorded.


Optical-alignment systems offer several advantages. Because laser fixtures eliminate the mechanical linkage and runout gauges, there is no fixture sag. This greatly increases the accuracy and repeatability of the data obtained when using this method.

Most of the optical-alignment systems incorporate a microprocessing unit, which eliminates recording errors commonly found with reverse-dial indicator and rim-and-face methods. Optical systems automatically maintain the proper orientation and provide accurate offset and angularity data, virtually eliminating operator error.

ill. 7.18 Typical optical or laser alignment system.

These microprocessor-based systems automatically calculate correction factors.

If the fixtures are properly mounted and the shafts are rotated to the correct positions, the system automatically calculates and displays the appropriate correction for each foot of the movable machine-train component. This feature greatly increases the accuracy of the alignment process.


Since optical-alignment systems are dependent on the transmission of a laser beam, which is a focused beam of light, they are susceptible to problems in some environments. Heat waves, steam, temperature variations, strong sunlight, and dust can distort the beam. When this happens, the system will not perform accurately.

One method that can be used to overcome most of the environment-induced problems is to use plastic tubing to shield the beam. This tubing can be placed between the transmitter and receiver of the optical-alignment fixture. It should be sized to permit transmission and reception of the light beam but small enough to prevent distortion caused by atmospheric or environmental conditions.

Typically, 2-inch, thin-wall tubing provides the protection required for most applications.


This section discusses the procedures for obtaining the measurements needed to align two classes of equipment: (1) horizontally installed units and (2) vertically installed units. The procedures for performing the initial alignment check for offset and angularity and for determining how much correction to make are presented.

Prior to taking alignment measurements, however, remember that it's necessary to remove any soft-foot that's present, making sure that the proper nut-tightening procedure is followed, and to correct for indicator sag (except when using the optical-alignment method). Refer to Section 2 for detailed discussions on indicator sag and soft-foot.

Horizontal Units

There are two parts to making alignment measurements on horizontally mounted units, and these are typically taken by using the reverse-dial indicator method. The first part of the procedure is to perform an initial alignment check by obtaining readings for the stationary and movable machines. The second part is to compare these values to the manufacturer's (i.e., desired) tolerances and to compute the difference between the actual readings and the desired readings.

The difference in the vertical readings is the amount of shim required to align the machine at the coupling for both vertical offset and angularity. The difference in the horizontal readings is the distance at the coupling to move the MTBM. These distances, however, must be converted to corrections to be made at the machine feet, computations that are made by using rise-and-run concepts.

ill. 7.19 Hypothetical present state, or actual, dial-indicator readings.

Initial Alignment Check

It is necessary to first obtain a complete set of indicator readings with the machines at ambient temperature, or non-operating condition. ill. 7.19 shows a hypothetical set of readings (i.e., top or 12 o'clock , right or 3 o'clock , bottom or 6 o'clock , and left or 9 o'clock ) taken for the stationary machine shaft

''A'' and the movable shaft ''B.'' The following is the procedure to be followed for obtaining these readings.

The indicator bar either must be free of sags or compensated for in the readings.

Check the coupling for concentricity. If not concentric, replace the coupling.

Zero the dial at top of the coupling.

Record the readings at 90-degree increments taken clockwise as indicated in ill. 7.19.

For any reading on a shaft, the algebraic sum of the left and right (9 and 3 o'clock ) must equal the top and bottom (12 and 6 o'clock ). The calculations below are for the example illustrated in ill. 7.19, in which shafts A and B are out of alignment as illustrated by the difference in the sums of the (L + R) readings for shafts A and B and the difference in the sums of the (T + B) readings for A and B.

Shaft A: Shaft B:

L1 + R1 = 12 + ( + 24) = 36 L2 + R2 = 26 + ( 22) = 48

T1 + B1 = 0 + ( + 36) = 36 T2 + B2 = 0 + ( 48) = 48

Note, however, that this difference, which represents the amount of misalignment at the coupling, is not the amount of correction needed to be performed at the machine feet. This must be determined by using rise-and-run concepts.

The dial indicator should start at midrange and not exceed the total range. In other words, don't peg the indicator. If misalignment exceeds the indicator span, it will be necessary to roughly align the machine before proceeding.

Determining Corrections or Amount of Shim

With horizontally mounted units, it's possible to correct both angularity and offset with one adjustment. To compute the adjustments needed to achieve the desired alignment, it's necessary to establish three horizontal measurements.

These measurements are critical to the success of any alignment and must be accurate to within 1.16 inch (see ill. 7.20). Again, the procedure described here is for the reverse-dial indicator method (see ill. 7.16).

1. Determine the distance, D1 , between the dial indicators.

2. It is also necessary to know the distance from the indicator plane of the stationary machine, or Machine ''A,'' to the near adjustment plane of the MTBM, or Machine ''B.'' This is the distance between the indicator planes of Machine ''A'' to the near foot (Nf ) of Machine

''B'' and is referred to as D2.

3. The distance between the indicator plane of Machine ''A'' to the far adjustment plane is needed. This distance is referred to as D3 and is the distance between the indicator plane of Machine ''A'' to the far foot (Ff ) of Machine ''B.''

The vertical and horizontal adjustments necessary to move Machine ''B'' from the actual position (ill. 7.19 readings) to the desired state of alignment (ill. 7.21 readings) are determined by using the equations below. Note that the desired state of alignment is obtained from manufacturer's tolerances. (When using manufacturer's tolerances, it's important to know if they compensate for thermal growth.) For example, the shim adjustment at the near foot (Nf ) and far foot (Ff ) for the readings in Figures 7.19 and 7.21 can be determined by using the vertical movement formulas shown below. Since the top readings equal zero, only the bottom readings are needed in the calculation.

ill. 7.20 Reverse-dial indicator alignment setup.

ill. 7.21 Desired dial indicator state readings at ambient conditions.

For Nf , at near foot of ''B,'' add 0.040-inch (40 mil) shims. For Ff , at the far foot of ''B,'' add 0.056-inch (56 mil) shims.

For example, the side-to-side movement at Nf and Ff can be determined in the horizontal movement formula:

For Nf , at near foot of ''B,'' move right 0.017 inch.

For Ff , at far foot of ''B,'' move right 0.050 inch.

Vertical Units

The alignment process for most vertical units is quite different from that used for aligning horizontally mounted units. The major reason is that most vertical units are not designed to allow realignment to be performed under the assumption that they will always fit together perfectly. Field checks, however, have proven this assumption to be wrong in a vast majority of cases. Although it's quite difficult to correct misalignment on a vertical unit, it's essential that it be done to increase reliability and decrease maintenance costs.

Initial Alignment Check

The following procedure can be used on vertical units to obtain angularity and offset values needed to compare with recommended manufacturer's (i.e., desired) tolerances to determine if a unit is out of alignment.

Perform an alignment check on the unit by using the reverse-dial indicator method.

Install brackets and dial indicators as illustrated in ill. 7.22.

Check the alignment in two planes by using the following directional designators: ''north/south'' and ''east/west.'' Consider the point of reference nearest to you as being ''south,'' which corresponds to the ''bottom'' position of a horizontal unit. (Note: Indicator sag does not occur when readings are taken as indicated below.) Perform the ''north/south'' alignment checks by setting the indicator dials to ''zero'' on the ''north'' side and take the readings on the ''south'' side.

Perform the ''east/west'' alignment checks by setting the indicator dials to ''zero'' on the ''west'' side and take the readings on the ''east'' side.

Record the distance between the dial indicator centerlines, D1.

Record the distance from the centerline of the coupling to the top dial indicator.

ill. 7.22 Proper dial indicator and bracket positioning when performing a vertical pump alignment.

Record ''zero'' for the distance, D2 , from the Indicator A to the ''top foot'' of the movable unit.

Record the distance, D3, from Indicator A to the ''bottom foot'' of the movable unit.

Set the top dial indicator to ''zero'' when it's in the ''north'' position.

North / South Alignment Check

Rotate shafts 180 degrees until the top indicator is in the ''south'' position and obtain a reading.

Rotate shafts 180 degrees again and check for repeatability of ''zero'' on the ''north'' side, then another 180 degrees to check for repeatability of reading obtained on the ''south'' side.

Note: If results are not repeatable, check bracket and indicators for looseness and correct as necessary. If repeatable, record the ''south'' reading.

Rotate the shafts until the bottom dial indicator is in the ''north'' position and set it to ''zero.'' Rotate the shafts 180 degrees and record ''south'' side reading. Check for repeatability.

East / West Alignment Check

Rotate the shafts until the top dial indicator is in the ''west'' position and set it to ''zero.'' Rotate the shafts 180 degrees and obtain the reading on the ''east'' side.

Check for repeatability.

Rotate the shafts until the bottom dial indicator is in the ''west'' position and set it to ''zero.'' Rotate the shafts 180 degrees and again obtain the reading on the ''east'' side. Check for repeatability.

Determining Corrections

If the unit must be realigned, with vertical units it's necessary to use the rim-and-face method to obtain offset and angularity readings. Unlike horizontally mounted units, it's not possible to correct both angularity and offset with one adjustment. Instead, we must first correct the angular misalignment in the unit by shimming and then correct the offset by properly positioning the motor base flange on the base plate.

Because most units are designed in such a manner that realignment is not intended, it's necessary to change this design feature. Specifically, the ''rabbet fit'' between the motor flange and the base plate is the major hindrance to realignment.

Therefore, before proceeding with the alignment method, one should consider that the rabbet fit is designed to automatically ''center'' the motor during installation.

In theory, this should create a condition of perfect alignment between the motor and the driven-unit shafts. The rabbet fit is not designed to support the weight of the unit or resist the torque during start-up or operation; the motor flange and hold-down bolts are designed to do this. Since the rabbet fit is merely a positioning device, it's quite permissible to ''bypass'' it. This may be accomplished by either of the following:

Machining off the entire male portion Grinding off the male and /or female parts as necessary.

Angularity Correction

There are three steps to follow when correcting for angularity. The first step is to obtain initial readings. The next step is to obtain corrected readings. The third step is to shim the machine.

ill. 7.23 Bottom dial indicator in position to obtain ''face readings.''

Step 1: Initial Readings : The following procedure is for obtaining initial readings.

Change the position of the bottom dial indicator so that it can obtain the ''face readings'' of the lower bracket (see ill. 7.23).

Looking from the ''south'' side, identify the hold-down bolt at the ''north'' position and label it #1. Proceeding clockwise, number each hold-down bolt until all are numbered (see ill. 7.24).

Determine the largest negative reading, which occurs at the widest point, by setting the bottom dial indicator to ''zero'' at point #1.

This should be in line with centerline of hold-down bolt #1. Record the reading.

Turn the shafts in a clockwise direction and record the data at each hold-down bolt centerline until readings have been taken at all positions.

Use ill. 7.25 as an example of how the readings are taken. Remember that all readings are taken from the position of looking down on the lower bracket.

Note: We will always be looking for the largest negative (-) reading. If all readings are positive ( + ), the initial set point of zero will be considered the largest negative (-) reading. In ill. 7.25, the largest negative reading occurs at point #7.

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ill. 7.24 Diagram of a base plate with hold-down bolts numbered.

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Step 2: Corrected Readings Obtain corrected readings with the following procedure.

Rotate the shafts until the indicator is again at the point where the largest negative reading occurs.

ill. 7.25 Determining the largest negative reading and the widest point.

Set the dial indicator to ''zero'' at this point and take another complete set of readings. With ill. 7.25 as an example, set the dial indicator to ''zero'' at point #7 (in line with centerline of bolt #7). The results of readings at the other hold-down bolt centerlines are as follows:

Step 3: Shimming Perform shimming with the following procedure. Measure the hold-down bolt circle radius and the radius of dial indicator travel as shown in ill. 7.26.

Compute the shim multiplier, X/Y, where: X = Bolt circle radius; = Radius of indicator ravel.

For example: If X = 9 inches and Y = 4 inches, the shim multiplier is 9/4 = 2.25.

The necessary shimming at each bolt equals the shim multiplier (2.25) times the bolt's corrected reading as determined in Section 4.

#1 - 2 25 16 = 36 mils = 0 036 inch

#2 - 2 25 23 = 52 mils = 0 052 inch

#3 - 2 25 32 = 72 mils = 0 072 inch

#4 - 2 25 24 = 54 mils = 0 054 inch

#5 - 2 25 17 = 38 mils = 0 038 inch

#6 - 2 25 8 = 18 mils = 0 018 inch

#7 - 2 25 0 = 0 mils = 0 000 inch

#8 - 2 25 7 = 16 mils = 0 016 inch

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ill. 7.26 Determining bolt circle radius and radius of dial indicator.

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Offset Correction: Once the angularity has been corrected by making the necessary shim adjustments at each of the hold-down bolts, it's necessary to correct the offset by sliding the movable unit (i.e., motor in this example) on the base plate. The top dial indicator is used to monitor the movements as they are being made. ''North/south'' and ''east/west'' designations are used to describe the positioning of the unit.

Nort h/ South Correction : The following is the procedure for making the ''north/south'' corrections.

Rotate shafts until the top dial indicator is in the ''north'' position. Set it to ''zero.'' Rotate the shafts 180 degrees (until the top dial indicator is in the ''south'' position) and record the reading.

Determine movement necessary to correct the offset in this plane by dividing the reading by 2. This is the amount of movement (in mils) required. Direction of movement can be determined by the following rule: If the sign of the reading is positive ( + ), the motor must be moved toward the ''north.'' If negative ( ), it must be moved toward the ''south.''

Eas t/ West Correction : The following is the procedure for making the ''east/west'' corrections.

Rotate the shafts until the top dial indicator is in the ''west'' position.

Set it to ''zero.'' Rotate the shafts 180 degrees (until the top dial indicator is in the ''east'' position) and record the reading.

Determine movement necessary to correct the offset in this plane by dividing the reading by 2. This value will be the amount of movement (in mils) required. Direction of movement can be determined by the following rule: If the sign of the reading is positive (+), the movable unit (motor) must be moved toward the ''west.'' If negative ( ), it must be moved toward the ''east.''

Making the Offset Corrections : After the amounts and directions of required offset adjustments have been obtained, the next step is to actually align the equipment. This is accomplished by using two dial indicators with magnetic bases, which are installed on the south (or north) and west (or east) sides of the mounting flange of the movable unit or motor. See ill. 7.27 for an illustration of this setup. It is important to zero both dial indicators before making adjustments and to watch both dial indicators while moving the unit.

Note: The motor position on the base plate must be adjusted to align the equipment, which may require machining or grinding of the rabbet fit. Remember, however, that the rabbet fit is only a positioning device and is not a structural support.


Once initial alignment readings are obtained by using the preceding procedures, they must be adjusted for changes in the machine-train, which can be caused by process movement, vibration, or thermal growth. These adjustments must be made to achieve proper alignment at normal operating conditions. Once readings are obtained, the use of graphical plotting helps the technician visualize misalignment and the necessary corrections that must be made and to catch computation errors.

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ill. 7.27 Placement of dial indicators to monitor offset corrections.

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Adjustments for Thermal Growth

Thermal growth generally refers to the expansion of materials with increasing temperature. For alignment purposes, thermal growth is the shaft centerline movement associated with the change in temperature from the alignment process, which is generally performed at ambient conditions, to normal operating conditions. Such a temperature difference causes the elevation of one or both shafts to change and misalignment to result. Temperature changes after alignment produce changes that may affect both offset and angularity of the shafts and can be in the vertical plane, horizontal plane, or any combination.

Proper alignment practices, therefore, must compensate for thermal growth.

In effect, the shafts must be misaligned in the ambient condition so they will become aligned when machine temperatures reach their normal operating range.

Generally, manufacturers supply dial indicator readings at ambient conditions, which compensate for thermal movement and result in colinear alignment at normal service conditions. When thermal rise information is supplied by the manufacturer or from machine history records, the necessary compensation may be made during the initial alignment procedure.

However, information concerning thermal rise is not available for all equipment.

Generally, manufacturers of critical machinery, such as centrifugal air compressors and turbines, will include information relating to thermal rise in their installation manuals in the section dealing with alignment. When this information is not available, the only method to determine the exact amount of compensation necessary to correct for thermal rise is referred to as a ''hot alignment check.''

Thermal Compensation Targets

A simple procedure for determining thermal compensation targets is to calculate the movement of the shaft due to temperature change at the bearings or feet.

Note that calculated thermal growth is highly dependent on the accuracy of the temperature assumptions and is useful only for initial alignment estimates.

Therefore the targets developed from the following procedure should be revised when better data become available.

The formula for this calculation is very simple and very accurate. It requires three factors: (1) the difference in temperature of the machine housing between the feet and shaft bearings, (2) the distance between the shaft centerline and the feet, and (3) the coefficient of thermal expansion of the machine housing material.

The thermal growth between any two points of any metal can be predicted by the formula:

Growth = D T L C Where:

D T = Temperature difference between the feet and shaft bearings, 8F L = Length between points (often the vertical distance from the shim plane to the shaft centerline), inches

C = Growth factor (coefficient of thermal expansion) Growth factors (mils/inch/8F) for common materials are:

Aluminum 0.0126 Bronze 0.0100 Cast Iron, Gray 0.0059 Stainless Steel 0.0074 Mild Steel, Ductile Iron 0.0063 Note: The thermal growth formula is usually applied only to the vertical components of the machine. While the formula can be applied to horizontal growth, this direction is often ignored.

For vertical growth, L is usually taken as the vertical height from the bottom of the foot where shims touch the machine to the shaft centerline. In the case where the machine is mounted on a base that has significant temperature variations along its length, L is the vertical distance from the concrete or other constant temperature baseline to the shaft centerline.

Hot Alignment Check

A hot alignment check is performed exactly like an ambient alignment check (see Section 4) with the added safety precautions required for hot machinery. The accuracy of a hot alignment check depends on how soon after shutdown dial indicator readings can be taken. Readings may be taken within a few minutes with the use of shaft-mounted brackets that span a flexible coupling. To speed up the process, assemble the brackets to the fullest extent possible prior to shutdown so that they need only be bolted to the shafts once the machine stops rotating.

Adjustments for Sag and Soft-Foot

The procedure for making adjustments to the readings to account for indicator sag is presented in Section 2.

ill. 7.28 Graphical plotting measurements .

Graphical Plotting

The graphical plotting technique for computing initial alignment can be per-formed with any of the three types of measurement fixtures (i.e., reverse-dial indicator, rim-and-face, or optical). The following steps should be followed when plotting alignment problems:

1. Determine the following dimensions from the machine-train, which are illustrated in ill. 7.28:

FBS = Front-foot to back-foot of stationary train component

CFS = Front-foot to coupling of stationary train component

CFM = Coupling to front-foot of movable train component

FBM = Front-foot to back-foot of movable train component

CD = Coupling or working diameter

2. On graph or grid paper, pick a horizontal line to be used as the baseline (also referred to as reference line or zero-lin e). This line usually crosses the center of the page from left to right and represents the rotational centerline of the stationary machine-train component.

3. Determine the number of inches or mils that each block on the graph paper represents by first finding the distance from the back-foot of the stationary component to the back-foot of the movable component.

Then determine the inches or mils per square that will spread the entire machine-train across the graph paper.

4. Plot inches or mils horizontally from left to right.

5. Plot mils from top to bottom vertically. As a general rule, assign 0.5, 1, 2, 5, 10 mils to each vertical step. Note that this scale may need to be changed in cases where excessive misalignment is present.

ill. 7.29 Graphical plotting of known foot correction.

Known Foot Correction Values

The following steps should be followed to plot misalignment when foot correc-tion values are known (see ill. 7.29):

1. On the baseline, start at the left end and mark the stationary back-foot.

From the back-foot and moving right, count the number of squares along the baseline corresponding to FFS. Mark the stationary front-foot location.

2. Starting at the stationary front-foot and moving right, count the number of squares along the baseline corresponding to CFS and mark the coupling location.

3. Continue this process until the entire machine-train is indicated on the graph.

4. To plot misalignment, locate the CFS or coupling on the horizontal baseline. From that point, count up or down on the vertical axis until the amount of offset is located on the mils scale. Mark this point on the graph. Use care to ensure that the location is accurately located.

Positive values should be above the horizontal baseline and negative values below the line.

5. Locate the FBM or back-foot of the movable component. Move either up or down vertically on the scale to the point of the offset measurement.

Mark this point on the graph. Remember, positive values are above the horizontal baseline and negative values below the line.

6. Draw a line from the back-foot (FBM) of the movable component or MTBM through the front-foot of the movable component toward the vertical line where the stationary coupling is located. Draw a short vertical line at the coupling end of the line. Finish the MTBM by drawing little squares to represent the feet, darkening the line from the back-foot to coupling, and darkening the coupling line.

ill. 7.30 Graphical plotting of known coupling results.

Known Coupling Results

When plotting coupling misalignment, use the following steps instead of those from the preceding section (see ill. 7.30).

1. Start at the stationary coupling location and , moving up or down the vertical axis (mils), count the number of squares corresponding to the vertical or horizontal offset. Move up for positive offset and down for negative offset. Mark a point, which is the MTBM coupling location.

2. Start at the MTBM coupling center and , moving right on the horizontal line, count the number of squares corresponding to the CD dimension (see ill. 7.28) and lightly mark the point. From this point, move up or down vertically on the mils scale the number of squares corresponding to the total mils of angularity per diameter (CD) and mark lightly.

3. From the MTBM coupling center, draw a line through the point marked in the preceding step and extending past the MTBM back-feet location. This line is the MTBM centerline.

4. Now place the MTBM feet. Starting at the MTBM coupling and moving right along a horizontal line, count the number of squares corresponding to CFM (see ill. 7.28). Then move straight vertically to the MTBM centerline and mark the location of the front-foot.

Then starting at the MTBM front-foot and moving right, count the number of squares corresponding to FBM. From this point, move vertically to the MTBM centerline and mark the location of the MTBM back-foot.

5. Draw a short line perpendicular to the shaft centerline to mark the MTBM coupling. Finish the MTBM by drawing little squares to represent the feet and darkening the line from the back-foot to the coupling.

6. Correction of the MTBM machine-train component can now be measured directly from the graph. Locate the appropriate MTBM foot location and read the actual correction from the vertical or mils scale.

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