Industrial Machinery Repair Part Episode 2 Part 3 potx

Rotation actionLine of Figure 14.7 Relationship of the pressure angle to the line of action It is extremely important that the pressure angle be known when gears aremated, as all gears t

Figure 14.2 Rack or straight-line gear

Figure 14.3 Typical spur gears

The sides of each tooth incline toward the center top at an angle called the

pressure angle, shown in Figure 14.5.

The 14.5-degree pressure angle was standard for many years In recent years,however, the use of the 20-degree pressure angle has been growing, andtoday 14.5-degree gearing is generally limited to replacement work Theprincipal reasons are that a 20-degree pressure angle results in a gear toothwith greater strength and wear resistance and permits the use of pinionswith fewer teeth The effect of the pressure angle on the tooth of a rack isshown in Figure 14.6

Rotation actionLine of

Figure 14.7 Relationship of the pressure angle to the line of action

It is extremely important that the pressure angle be known when gears aremated, as all gears that run together must have the same pressure angle.The pressure angle of a gear is the angle between the line of action and theline tangent to the pitch circles of mating gears Figure 14.7 illustrates therelationship of the pressure angle to the line of action and the line tangent

to the pitch circles

Pitch Diameter and Center Distance

Pitch circles have been defined as the imaginary circles that are in contactwhen two standard gears are in correct mesh The diameters of these circlesare the pitch 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 twopitch diameters, as shown in Figure 14.8

This relationship may also be stated in an equation, and may be simplified

by using letters to indicate the various values, as follows:

C= center distance

Figure 14.8 Pitch diameter and center distance

Centerdistance (C)

Circular pitch

Figure 14.10 Circular pitch

Circular Pitch

A specific type of pitch designates the size and proportion of gear teeth

In gearing terms, there are two specific types of pitch: circular pitch and diametrical pitch Circular pitch is simply the distance from a point on

one tooth to a corresponding point on the next tooth, measured along thepitch line or circle, as illustrated in Figure 14.10 Large-diameter gears arefrequently made to circular pitch dimensions

Diametrical Pitch and Measurement

The diametrical pitch system is the most widely used, as practically allcommon-size gears are made to diametrical pitch dimensions It designatesthe size and proportions of gear teeth by specifying the number of teeth inthe gear for each inch of the gear’s pitch diameter For each inch of pitchdiameter, there are pi (π) inches, or 3.1416 inches, of pitch-circle circumfer-

ence The diametric pitch number also designates the number of teeth foreach 3.1416 inches of pitch-circle circumference Stated in another way, the

diametrical pitch number specifies the number of teeth in 3.1416 inches

along the pitch line of a gear

For simplicity of illustration, a whole-number pitch-diameter gear (4 inches),

is shown in Figure 14.11

Figure 14.11 illustrates that thediametrical pitch number specifying the

number of teeth per inch of pitch diameter must also specify the number ofteeth per 3.1416 inches of pitch-line distance This may be more easily visual-ized and specifically dimensioned when applied to the rack in Figure 14.12

Figure 14.12 Number of teeth in 3.1416 inches

Because the pitch line of a rack is a straight line, a measurement can beeasily made along it In Figure 14.12, it is clearly shown that there are 10teeth in 3.1416 inches; therefore the rack illustrated is a 10 diametrical pitchrack

A similar measurement is illustrated in Figure 14.13, along the pitch line of

a gear The diametrical pitch being the number of teeth in 3.1416 inches ofpitch line, the gear in this illustration is also a 10 diametrical pitch gear

In many cases, particularly on machine repair work, it may be desirablefor the mechanic to determine the diametrical pitch of a gear This may bedone very easily without the use of precision measuring tools, templates, orgauges Measurements need not be exact because diametrical pitch numbers

Figure 14.13 Number of teeth in 3.1416 inches on the pitch circle

are usually whole numbers Therefore, if an approximate calculation results

in a value close to a whole number, that whole number is the diametricalpitch number of the gear

The following two methods may be used to determine the approximate metrical pitch of a gear A common steel rule, preferably flexible, is adequate

dia-to make the required measurements

Method 1

Count the number of teeth in the gear, add 2 to this number, and divide

by the outside diameter of the gear Scale measurement of the gear to theclosest fractional size is adequate accuracy

Figure 14.14 illustrates a gear with 56 teeth and an outside measurement of

513

16 inches Adding 2 to 56 gives 58; dividing 58 by 513

16 gives an answer

of 93132 Since this is approximately 10, it can be safely stated that the gear

is a 10 diametrical pitch gear

Method 2

Count the number of teeth in the gear and divide this number by the sured pitch diameter The pitch diameter of the gear is measured from theroot or bottom of a tooth space to the top of a tooth on the opposite side

mea-of the gear

Figure 14.15 illustrates a gear with 56 teeth The pitch diameter measuredfrom the bottom of the tooth space to the top of the opposite tooth is 558inches Dividing 56 by 558 gives an answer of 915

16 inches, or approximately

10 This method also indicates that the gear is a 10 diametrical pitch gear

num-P= N

36 teeth?

D= N

12 or D= 3" pitch diameterExample 3: How many teeth are there in a 16diametrical pitch gear with a

pitch diameter of 33

4 inches?

N= D × P or N = 33

4× 16 or N = 60 teethCircular pitch is the distance from a point on a gear tooth to the correspond-ing point on the next gear tooth measured along the pitch line Its value

is equal to the circumference of the pitch circle divided by the number ofteeth in the gear The relationship of the circular pitch to thepitch-circle circumference, number of teeth, and the pitch diameter may also be stated

Example 1: What is thecircular pitch of a gear with 48 teeth and a pitch diameter of 6"?

128 teeth?

D= pNπ or .5× 128

3 1416 D= 20.371 inchesThe list that follows offers just a few names of the various parts given togears These parts are shown in Figures 14.16 and 14.17

● Addendum: Distance the tooth projects above, or outside, the pitch line

Addendum

Dedendum Whole

depth

Circularpitch

Figure 14.17 Names of rack parts

● 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 tooth space

● Working Depth: The depth of tooth engagement of two matching gears

It is the sum of their addendums

● Tooth Thickness: The distance along the pitch line or circle from one side

of a gear tooth to the other

Tooth Proportions

The fulldepth involute system is the gear system in most common use The

formulas (with symbols) shown below are used for calculating tooth portions of full-depth involute gears Diametrical pitch is given the symbol

pro-P as before

Addendum, a= 1

PWhole depth, Wd= 20+ 0 002

P (20P or smaller)Dedendum, Wd= 2.157

P (larger than 20P)Whole depth, b= Wd − a

Clearance, c= b − aTooth thickness, t= 1 5708

P

Backlash

Backlash in gears is the play between teeth that prevents binding In terms

of tooth dimensions, it is the amount by which the width of tooth spacesexceeds the thickness of the mating gear teeth Backlash may also bedescribed as the distance, measured along the pitch line, that a gear

run-On nonreversing 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.

Other Gear Types

Many styles and designs of gears have been developed from the spur gear.While they are all commonly used in industry, many are complex in designand manufacture Only a general description and explanation of principleswill be given, as the field of specialized gearing is beyond the scope of thisbook Commonly used styles will be discussed sufficiently to provide themillwright or mechanic with the basic information necessary to performinstallation and maintenance work

Bevel and Miter

Two major differences between bevel gears and spur gears are their shapeand the relation of the shafts on which they are mounted The shape of aspur gear is essentially a cylinder, while the shape of a bevel gear is a cone.Spur gears are used to transmit motion between parallel shafts, while bevelgears transmit motion between angular or intersecting shafts The diagram

in Figure 14.19 illustrates the bevel gear’s basic cone shape Figure 14.20shows a typical pair of bevel gears

Special bevel gears can be manufactured to operate at any desired shaftangle, as shown in Figure 14.21 Miter gears are bevel gears with the samenumber of teeth in both gears operating on shafts at right angles or at

90 degrees, as shown in Figure 14.22

A typical pair of straight miter gears is shown in Figure 14.23 Another style

of miter gears having spiral rather than straight teeth is shown in Figure14.24 The spiral-tooth style will be discussed later

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

of bevel gears Because the tooth size varies along its length, it must bemeasured at a given point This point is the outside part of the gear wherethe tooth is the largest Because each gear in a set of bevel gears must havethe same angles and tooth lengths, as well as the same diametrical pitch,they are manufactured and distributed only in mating pairs Bevel gears,

Figure 14.19 Basic shape of bevel gears

Figure 14.20 Typical set of bevel gears

Shaft angle

Figure 14.21 Shaft angle, which can be at any degree

like spur gears, are manufactured in both the 14.5-degree and 20-degreepressure-angle designs

Helical

Helical gears are designed for parallel-shaft operation like the pair inFigure 14.25 They are similar to spur gears except that the teeth are cut at anangle to the centerline The principal advantage of this design is the quiet,smooth action that results from the sliding contact of the meshing teeth

A disadvantage, however, is the higher friction and wear that accompanies

Figure 14.22 Miter gears, which are shown at 90 degrees

Figure 14.23 Typical set of miter gears

this sliding action The angle at which the gear teeth are cut is called the

helix angle and is illustrated in Figure 14.25.

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

be either a “right-hand” or a “left-hand” helix The hand of the helix is thesame regardless of how it is viewed Figure 14.26 illustrates a helical gear as

Figure 14.24 Miter gears with spiral teeth

viewed from opposite sides; changing the position of the gear cannot changethe hand of the tooth’s helix angle A pair of helical gears, as illustrated inFigure 14.27, must have the same pitch and helix angle but must be ofopposite hands (one right hand and one left hand)

Helical gears may also be used to connect nonparallel shafts When usedfor this purpose, they are often called “spiral” gears or crossed-axis helicalgears This style of helical gearing is shown in Figure 14.28

Worm

The worm and worm gear, illustrated in Figure 14.29, are used to transmitmotion and power when a high-ratio speed reduction is required Theyprovide a steady quiet transmission of power between shafts at right angles.The worm is always the driver and the worm gear the driven member Likehelical gears, worms and worm gears have “hand.” The hand is determined

by the direction of the angle of the teeth Thus, in order for a worm andworm gear to mesh correctly, they must be the same hand

Figure 14.25 Typical set of helical gears

Helixangle

Figure 14.26 Illustrating the angle at which the teeth are cut

The most commonly used worms have either one, two, three, or four arate threads and are called single, double, triple, and quadruple threadworms The number of threads in a worm is determined by counting thenumber of starts or entrances at the end of the worm The thread of the

Hub on

left side

Hub onright side

Figure 14.27 Helix angle of the teeth the same regardless of side from which the gear is viewed

Figure 14.28 Typical set of spiral gears

Figure 14.29 Typical set of worm gears

worm is an important feature in worm design, as it is a major factor in wormratios The ratio of a mating worm and worm gear is found by dividing thenumber of teeth in the worm gear by the number of threads in the worm

Herringbone

To overcome the disadvantage of the high end thrust present in helical gears,the herringbone gear, illustrated in Figure 14.30, was developed It consistssimply of two sets of gear teeth, one right-hand and one left-hand, on thesame gear The gear teeth of both hands cause the thrust of one set to cancelout the thrust of the other Thus, the advantage of helical gears is obtained,and quiet, smooth operation at higher speeds is possible Obviously theycan only be used for transmitting power between parallel shafts

Gear Dynamics and Failure Modes

Many machine trains utilize gear drive assemblies to connect the driver tothe primary machine Gears and gearboxes typically have several vibrationspectra associated with normal operation Characterization of a gearbox’s

Figure 14.30 Herringbone gear

vibration signature box is difficult to acquire but is an invaluable tool fordiagnosing machine-train problems The difficulty is that: (1) it is oftendifficult to mount the transducer close to the individual gears and (2) thenumber of vibration sources in a multigear drive results in a complex assort-ment of gear mesh, modulation, and running frequencies Severe drive-trainvibrations (gearbox) are usually due to resonance between a system’s nat-ural frequency and the speed of some shaft The resonant excitation arisesfrom, and is proportional to, gear inaccuracies that cause small periodicfluctuations in pitch-line velocity Complex machines usually have manyresonance zones within their operating speed range because each shaft canexcite a system resonance At resonance these cyclic excitations may causelarge vibration amplitudes and stresses

Basically, forcing torque arising from gear inaccuracies is small However,under resonant conditions torsional amplitude growth is restrained only

by damping in that mode of vibration In typical gearboxes this damping isoften small and permits the gear-excited torque to generate large vibrationamplitudes under resonant conditions

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 direc-tion, radial or axial, of the thrust load of typical gear-sets will provide some