Maintenance Fundamentals 2011 Part 8 pot

Figure 11.7 illustrates the relationship of thepressure angle to the line of action and the line tangent to the pitch circles.PITCHDIAMETERANDCENTERDISTANCE Pitch circles have been defin

pitch circles of mating gears Figure 11.7 illustrates the relationship of thepressure angle to the line of action and the line tangent to the pitch circles.

PITCHDIAMETERANDCENTERDISTANCE

Pitch circles have been defined as the imaginary circles that are in contact whentwo standard gears are in correct mesh The diameters of these circles are thepitch diameters of the gears The center distance of the two gears, therefore,when correctly meshed, is equal to one half of the sum of the two pitch diam-eters, as shown in Figure 11.8

This relationship may also be stated in an equation and may be simplified byusing letters to indicate the various values, as follows:

Figure 11.6 Different pressure angles on gear teeth

Figure 11.7 Relationship of the pressure angle to the line of action

C ¼ Center distance

D1¼ First pitch diameter

D2¼ Second pitch diameter

as illustrated in Figure 11.10 Large-diameter gears are frequently made tocircular pitch dimensions

Figure 11.8 Pitch diameter and center distance

Figure 11.9 Determining center distance

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DIAMETRICALPITCH ANDMEASUREMENT

The diametrical pitch system is the most widely used, as practically all sized gears are made to diametrical pitch dimensions It designates the size andproportions of gear teeth by specifying the number of teeth in the gear for eachinch of the gear’s pitch diameter For each inch of pitch diameter, there are pi (p)inches, or 3.1416 in., of pitch-circle circumference The diametric pitch numberalso designates the number of teeth for each 3.1416 in of pitch-circle circumfer-ence Stated in another way, the diametrical pitch number specifies the number

common-of teeth in 3.1416 in along the pitch line common-of a gear

For simplicity of illustration, a whole-number pitch-diameter gear (4 in.), isshown in Figure 11.11

Figure 11.11 illustrates that the diametrical pitch number specifying thenumber of teeth per inch of pitch diameter must also specify the number of

Figure 11.10

Figure 11.11 Pitch diameter and diametrical pitch

teeth per 3.1416 in of pitch-line distance This may be more easily visualized andspecifically dimensioned when applied to the rack in Figure 11.12.

Because the pitch line of a rack is a straight line, a measurement can be easilymade along it In Figure 11.12, it is clearly shown that there are 10 teeth in3.1416 in.; therefore the rack illustrated is a 10 diametrical pitch rack

A similar measurement is illustrated in Figure 11.13, along the pitch line of agear The diametrical pitch being the number of teeth in 3.1416 in of pitch line,the gear in this illustration is also a 10 diametrical pitch gear

In many cases, particularly in machine repair work, it may be desirable for themechanic to determine the diametrical pitch of a gear This may be done veryeasily without the use of precision measuring tools, templates, or gauges Meas-urements need not be exact because diametrical pitch numbers are usually wholenumbers Therefore, if an approximate calculation results in a value close to awhole number, that whole number is the diametrical pitch number of the gear

The following three methods may be used to determine the approximate rical pitch of a gear A common steel rule, preferably flexible, is adequate tomake the required measurements

diamet-Figure 11.12 Number of teeth in 3.1416 in

Figure 11.13 Number of teeth in 3.1416 in on the pitch circle

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Count the number of teeth in the gear, add 2 to this number, and divide by theoutside diameter of the gear Scale measurement of the gear to the closest fractionalsize is adequate accuracy

Figure 11.14 illustrates a gear with 56 teeth and an outside measurement of5⁄13

16 in Adding 2 to 56 gives 58; dividing 58 by 5-13⁄16gives an answer of 9-31⁄32.Since this is approximately 10, it can be safely stated that the gear is a 10 decimalpitch gear

Count the number of teeth in the gear and divide this number by the measuredpitch diameter The pitch diameter of the gear is measured from the root orbottom of a tooth space to the top of a tooth on the opposite side of the gear.Figure 11.15 illustrates a gear with 56 teeth The pitch diameter measured fromthe bottom of the tooth space to the top of the opposite tooth is 5-5⁄8 in Dividing

56 by 5-5⁄8 gives an answer of 9-15⁄16 in or approximately 10 This method alsoindicates that the gear is a 10 decimal pitch gear

PITCHCALCULATIONS

Diametrical pitch, usually a whole number, denotes the ratio of the number ofteeth to a gear’s pitch diameter Stated another way, it specifies the number ofteeth in a gear for each inch of pitch diameter The relationship of pitch

Figure 11.14 Use of Method 1 to approximate the diametrical pitch In this method theoutside diameter of the gear is measured

diameter, diametrical pitch, and number of teeth can be stated mathematically asfollows.

D¼N

P or D¼36

12 or D¼ 3-in: pitch diameterExample 3: How many teeth are there in a 16 diametrical pitch gear with a pitchdiameter of 3–3⁄ in.?

Figure 11.15 Use of Method 2 to approximate the diametrical pitch This method usesthe pitch diameter of the gear

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Circumference of pitch circle¼ pD

P¼
D

Pwhere,

D¼PN

p or

:5 1283:1416 D¼ 20:371 inchesThe list that follows contains just a few names of the various parts given to gears.These parts are shown in Figures 11.16 and 11.17

 Addendum: Distance the tooth projects above, or outside, the pitchline or circle

 Dedendum: Depth of a tooth space below, or inside, the pitch line orcircle

 Clearance: Amount by which the dedendum of a gear tooth exceeds theaddendum of a matching gear tooth.

 Whole Depth: The total height of a tooth or the total depth of a toothspace

 Working Depth: The depth of tooth engagement of two matchinggears It is the sum of their addendums

 Tooth Thickness: The distance along the pitch line or circle from oneside of a gear tooth to the other

The full-depth involute system is the gear system in most common use Theformulas (with symbols) shown below are used for calculating tooth proportions

of full-depth involute gears Diametrical pitch is given the symbol P as before

Figure 11.16 Names of gear parts

Figure 11.17 Names of rack parts

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Addendum, a¼1

PWhole Depth, Wd¼2:0þ :002

P (20P or smaller)Dedendum, Wd ¼2:157

P (Larger than 20P)Whole Depth, b¼ Wd
a

A small amount of backlash is also desirable because of the dimensional ations involved in practical manufacturing tolerances

vari-Backlash is built into standard gears during manufacture by cutting the gear teeththinner than normal by an amount equal to one half the required figure When twogears made in this manner are run together, at standard center distance, theirallowances combine, provided the full amount of backlash is required

Figure 11.18 Backlash

On non-reversing drives or drives with continuous load in one direction, theincrease in backlash that results from tooth wear does not adversely affectoperation However, on reversing drive and drives where timing is critical,excessive backlash usually cannot be tolerated.

OTHERGEARTYPES

Many styles and designs of gears have been developed from the spur gear Whilethey are all commonly used in industry, many are complex in design andmanufacture Only a general description and explanation of principles will begiven, as the field of specialized gearing is beyond the scope of this book.Commonly used styles will be discussed sufficiently to provide the millwright

or mechanic with the basic information necessary to perform installation andmaintenance work

BEVEL ANDMITER

Two major differences between bevel gears and spur gears are their shape and therelation of the shafts on which they are mounted The shape of a spur gear isessentially a cylinder, while the shape of a bevel gear is a cone Spur gears areused to transmit motion between parallel shafts, while bevel gears transmitmotion between angular or intersecting shafts The diagram in Figure 11.19illustrates the bevel gear’s basic cone shape Figure 11.20 shows a typical pair

The diametrical pitch number as is done with spur gears establishes the tooth size

of bevel gears Because the tooth size varies along its length, it must be measured

at a given point This point is the outside part of the gear where the tooth is thelargest Because each gear in a set of bevel gears must have the same angles andtooth lengths, as well as the same diametrical pitch, they are manufactured anddistributed only in mating pairs Bevel gears, like spur gears, are manufactured inboth the 14.5-degree and 20-degree pressure-angle designs

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Figure 11.19 Basic shape of bevel gears.

Figure 11.20 Typical set of bevel gears

Figure 11.21 Shaft angle, which can be at any degree.

Figure 11.22 Miter gears, which are shown at 90 degrees

HELICAL

Helical gears are designed for parallel-shaft operation like the pair in Figure 11.25.They are similar to spur gears except that the teeth are cut at an angle to thecenterline The principal advantage of this design is the quiet, smooth action thatresults from the sliding contact of the meshing teeth A disadvantage, however, is thehigher friction and wear that accompanies this sliding action The angle at which thegear teeth are cut is called the helix angle and is illustrated in Figure 11.26

It is very important to note that the helix angle may be on either side of the gear’scenterline Or if compared with the helix angle of a thread, it may be either a

‘‘right-hand’’ or a ‘‘left-hand’’ helix The hand of the helix is the same regardless

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of how viewed Figure 11.27 illustrates a helical gear as viewed from oppositesides; changing the position of the gear cannot change the hand of the tooth’shelix angle A pair of helical gears, as illustrated in Figure 11.25, must have thesame pitch and helix angle but must be of opposite hands (one right hand andone left hand).

Helical gears may also be used to connect nonparallel shafts When used for thispurpose, they are often called ‘‘spiral’’ gears or crossed-axis helical gears Thisstyle of helical gearing is shown in Figure 11.28

WORM

The worm and worm gear, illustrated in Figure 11.29, are used to transmitmotion and power when a high-ratio speed reduction is required They provide

a steady quiet transmission of power between shafts at right angles The worm is

Figure 11.23 Typical set of miter gears

Figure 11.24 Miter gears with spiral teeth.

Figure 11.25 Typical set of helical gears

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Figure 11.26 The angle at which teeth are cut.

Figure 11.27 Helix angle of teeth: the same no matter from which side the gear is viewed

Figure 11.28 Typical set of spiral gears

Figure 11.29 Typical set of worm gears.

always the driver and the worm gear the driven member Like helical gears,worms and worm gears have ‘‘hand.’’ The hand is determined by the direction ofthe angle of the teeth Thus, for a worm and worm gear to mesh correctly, theymust be the same hand

The most commonly used worms have either one, two, three, or four separatethreads and are called single, double, triple, and quadruple thread worms Thenumber of threads in a worm is determined by counting the number of starts orentrances at the end of the worm The thread of the worm is an important feature

in worm design, as it is a major factor in worm ratios The ratio of a matingworm and worm gear is found by dividing the number of teeth in the worm gear

by the number of threads in the worm

To overcome the disadvantage of the high end thrust present in helical gears, theherringbone gear, illustrated in Figure 11.30, was developed It consists simply oftwo sets of gear teeth, one right hand and one left hand, on the same gear Thegear teeth of both hands cause the thrust of one set to cancel out the thrust of

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the other Thus the advantage of helical gears is obtained, and quiet, smoothoperation at higher speeds is possible Obviously they can only be used fortransmitting power between parallel shafts.

GEARDYNAMICSANDFAILUREMODES

Many machine-trains utilize gear drive assemblies to connect the driver to theprimary machine Gears and gearboxes typically have several vibration spectraassociated with normal operation Characterization of a gearbox’s vibrationsignature box is difficult to acquire but is an invaluable tool for diagnosingmachine-train problems The difficulty is that (1) it is often difficult to mountthe transducer close to the individual gears, and (2) the number of vibrationsources in a multi-gear drive results in a complex assortment of gear mesh,modulation, and running frequencies Severe drive-train vibrations (gearbox)are usually due to resonance between a system’s natural frequency and thespeed of some shaft The resonant excitation arises from, and is proportional

to, gear inaccuracies that cause small periodic fluctuations in pitch-line velocity.Complex machines usually have many resonance zones within their operatingspeed range because each shaft can excite a system resonance At resonance thesecyclic excitations may cause large vibration amplitudes and stresses

Basically, forcing torque arising from gear inaccuracies is small However, underresonant conditions torsional amplitude growth is restrained only by damping inthat mode of vibration In typical gearboxes this damping is often small andpermits the gear-excited torque to generate large vibration amplitudes underresonant conditions

Figure 11.30 Herringbone gear

One other important fact about gear sets is that all gear sets have a designedpreload and create an induced load (thrust) in normal operation The direction,radial or axial, of the thrust load of typical gear sets will provide some insightinto the normal preload and induced loads associated with each type of gear.

To implement a predictive maintenance program, a great deal of time should bespent understanding the dynamics of gear/gearbox operation and the frequenciestypically associated with the gearbox As a minimum, the following should beidentified

Gears generate a unique dynamic profile that can be used to evaluate gearcondition In addition, this profile can be used as a tool to evaluate the operatingdynamics of the gearbox and its related process system

Normal Profile

In a normal gear set, each of the side bands will be spaced at exactly the 1Xrunning speed of the input shaft, and the entire gear mesh will be symmetrical Inaddition, the side bands will always occur in pairs, one below and one above thegear mesh frequency The amplitude of each of these pairs will be identical Forexample, the side band pair indicated as
1 and þ1 in Figure 11.31 will bespaced at exactly input speed and have the same amplitude

If the gear mesh profile were split by drawing a vertical line through the actualmesh (i.e., number of teeth times the input shaft speed), the two halves would beexactly identical Any deviation from a symmetrical gear mesh profile is indica-tive of a gear problem However, care must be exercised to ensure that theproblem is internal to the gears and induced by outside influences Externalmisalignment, abnormal induced loads, and a variety of other outside influenceswill destroy the symmetry of the gear mesh profile For example, the singlereduction gearbox used to transmit power to the mold oscillator system on acontinuous caster drives two eccentrics The eccentric rotation of these twocams is transmitted directly into the gearbox and will create the appearance of

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