Maintenance Fundamentals Episode 2 part 1 potx

Figure 11.7 illustrates the relationship of the pressure angle to the line of action and the line tangent to the pitch circles.. The center distance of the two gears, therefore, when cor

Hubs H/2

Y Shafts

T D

D S

2

T = D - Y + H + C H/2

2

S = D - Y - H

Figure 10.17 Shaft and hub dimensions

Table 10.2 Standard Square Keys and Keyways (inches)*

Diameter Of Holes

(Inclusive)

Keyways

Key Stock

5 ⁄16to 7 ⁄16 3 ⁄32 3 ⁄64 3 ⁄32 3 ⁄32

1

⁄ 2 to9⁄ 16 1⁄ 8 1⁄ 16 1⁄ 8 1⁄ 8

5

⁄ 16

15 ⁄ 16 to 1- 1 ⁄ 4 1⁄ 4 1⁄ 8 1⁄ 4  1 ⁄ 4

1-5⁄ 16 to 1-3⁄ 8 5⁄ 16 5⁄ 32 5⁄ 16 5⁄ 16

1-7⁄ 16 to 1-3⁄ 4 3⁄ 8 3⁄ 16 3⁄ 8  3

⁄ 8 1- 13 ⁄ 16 to 2- 1 ⁄ 4 1⁄ 2 1⁄ 4 1⁄ 2  1 ⁄ 2

2-5⁄ 16 to 2-3⁄ 4 5⁄ 8 5⁄ 16 5⁄ 8 5⁄ 8

2-13⁄ 16 to 3-1⁄ 4 3⁄ 4 3⁄ 8 3⁄ 4  3

⁄ 4 3- 5 ⁄ 16 to 3- 3 ⁄ 4 7⁄ 8 7⁄ 16 7⁄ 8  7 ⁄ 8

*Square keys are normally used through shaft diameter 4-1⁄ 2 in.; larger shafts normally use flat keys.

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

D2 W2

p 2 where:

C¼ Allowance or clearance for key, inches

D¼ Nominal shaft or bore diameter, inches

Table 10.3 Standard Flat Keys and Keyways (inches)

Diameter Of Holes

(Inclusive)

Keyways

Key Stock

1

⁄ 2 to9⁄ 16 00 1

⁄ 8 3⁄ 64 1⁄ 8 1⁄ 32

5 ⁄ 8 to 7 ⁄ 8 00 3 ⁄ 16 1⁄ 16 3⁄ 16  1 ⁄ 8

15 ⁄ 16 to 1- 1 ⁄ 4 00 1 ⁄ 4 3⁄ 32 1⁄ 4  3 ⁄ 16

1- 5 ⁄16to 1- 3 ⁄800 5 ⁄16 1 ⁄8 5 ⁄16 1 ⁄4

1-7⁄ 16 to 1-3⁄ 4 00 3

⁄ 4 1-13⁄ 16 to 2-1⁄ 4 00 1

⁄ 2 3⁄ 16 1⁄ 2 3⁄ 8 2- 5 ⁄ 16 to 2- 3 ⁄ 4 00 5 ⁄ 8 7⁄ 32 5⁄ 8  7 ⁄ 16

2- 13 ⁄ 16 to 3- 1 ⁄ 4 00 3 ⁄ 4 1⁄ 4 3⁄ 4  1 ⁄ 2

3- 5 ⁄16to 3- 3 ⁄400 7 ⁄8 5 ⁄16 7 ⁄8 5 ⁄8

3-13⁄ 16 to 4-1⁄ 2 00 1 3⁄ 8 1  3

⁄ 4 4-9⁄ 16 to 5-1⁄ 2 00 1-1⁄ 4 7⁄ 16 11⁄ 4 7⁄ 8

5- 9 ⁄ 16 to 6- 1 ⁄ 2 00 1- 1 ⁄ 2 1⁄ 2 1- 1 ⁄ 2  1

6- 9 ⁄16to 7- 1 ⁄200 1- 3 ⁄4 5 ⁄8 1- 3 ⁄4 1 ⁄4

⁄ 4 9-1⁄ 16 to 1100 2-1⁄ 2 7⁄ 8 2-1⁄ 2  1- 3

⁄ 4

13- 1 ⁄ 16 to 15 00 3- 1 ⁄ 2 1- 1 ⁄ 4 3- 1 ⁄ 2  2- 1 ⁄ 2

18-1⁄ 16 to 2200 5 1-3⁄ 4 5  3 1

⁄ 2

Source: The Falk Corporation.

H ¼ Nominal key height, inches

W¼ Nominal key width, inches

Y ¼ Chordal height, inches

Note: Tables shown below are prepared for manufacturing use Dimensions given are for standard shafts and keyways

KEYWAYMANUFACTURINGTOLERANCES

Keyway manufacturing tolerances (illustrated in Figure 10.18) are referred to as offset (centrality) and lead (cross axis) Offset or centrality is referred to as Dimension ‘‘N’’; lead or cross axis is referred to as Dimension ‘‘J.’’ Both must

be kept within permissible tolerances, usually 0.002 in

Offset or Centrality

Shaft

Bore

Keyseat

A

N

Lead or Cross Axis

Shaft

Keyseat

Lead Lead

B

Figure 10.18 Manufacturing tolerances A, Offset B, Lead

Calculations for shear and compressive key stresses are based on the following assumptions:

1 The force acts at the radius of the shaft

2 The force is uniformly distributed along the key length

3 None of the tangential load is carried by the frictional fit between shaft and bore

The shear and compressive stresses in a key are calculated using the following equations (see Figure 10.19):

(d) (w)  (L) Sc¼

2T (d) (h1) (L) where:

d ¼ Shaft diameter, inches (use average diameter for taper shafts)

h1 ¼ Height of key in the shaft or hub that bears against the keyway,

inches Should equal h2 for square keys For designs where unequal portions of the key are in the hub or shaft, h1 is the minimum portion

L ¼ Effective length of key, inches

RPM¼ Revolutions per minute

Ss ¼ Shear stress, psi

Sc ¼ Compressive stress, psi

T ¼ Shaft torque, lb-in orHp 63000

RPM

w ¼ Key width, inches

Figure 10.19 Measurements used in calculating shear and compressive key stress

Key material is usually AISI 1018 or AISI 1045 Table 10.4 provides the allow-able stresses for these materials

Example: Select a key for the following conditions: 300 Hp at 600 RPM; 3-inch diameter shaft,3⁄4-inch3⁄4-inch key, 4-inch key engagement length

T¼ Torque ¼Hp 63; 000

600 ¼ 31; 500 in-lbs

d w  L¼

2 31; 500

3 3=4  4¼ 7; 000 psi

d h1 L¼

2 31; 500

3 3=8  4¼ 14; 000 psi The AISI 1018 key can be used since it is within allowable stresses listed in Table 10.4 (allowable Ss¼ 7,500, allowable Sc ¼ 5,000)

Note: If shaft had been 2-3⁄4-in diameter (4-in hub), the key would be5⁄8-in.

5⁄8-in., Ss¼ 9,200 psi, Sc ¼ 18,400 psi, and a heat-treated key of AISI 1045 would have been required (allowable Ss¼ 15,000, allowable Sc ¼ 30,000)

SHAFTSTRESSCALCULATIONS

Torsional stresses are developed when power is transmitted through shafts In addition, the tooth loads of gears mounted on shafts create bending stresses Shaft design, therefore, is based on safe limits of torsion and bending

To determine minimum shaft diameter in inches:

Minimum Shaft Diameter¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Hp 321000 RPM Allowable Stress 3

r

Table 10.4 Allowable Stresses for AISI 1018 and AISI 1045

Material

Heat Treatment

Allowable Stresses – psi Shear Compressive

AISI 1045 255-300 Bhn 15,000 30,000

Hp¼ 300

RPM¼ 30

Material¼ 225 Brinell

From Figure 10.20 at 225 Brinell, Allowable Torsion¼ 8000 psi

Minimum Shaft Diameter¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

300 321000

30 8000 3

r

¼ ffiffiffiffiffiffiffiffi 402 3 p

¼ 7:38 inches

From Table 10.5, note that the cube of 7-1⁄4 in is 381, which is too small (i.e.,

<402) for this example The cube of 7-1⁄2 in is 422, which is large enough

To determine shaft stress, psi:

Shaft Stress¼Hp 321; 000

RPM d3

TENSILE STRENGTH, 1000 PSI (APPROX.)

BRINELL HARDNESS

80

20000

16000

12000

8000

24000

4000

Bending

Torsion

Figure 10.20 Allowable stress as a function of Brinell hardness

Example: Given 7-1⁄2-in shaft for 300 Hp at 30 RPM

Shaft Stress¼300 321; 000

30 (7  1=2)3 ¼ 7; 600 psi Note: The 7-1⁄4-in diameter shaft would be stressed to 8420 psi

Table 10.5 Shaft Diameters (Inches) and Their Cubes (Cubic Inches)

1-3⁄ 4 5.36 5-3⁄ 4 190.1 10-1⁄ 2 1157

2-1⁄ 4 11.39 6-1⁄ 4 244 11-1⁄ 2 1520

2- 3 ⁄4 20.80 6- 3 ⁄4 308 12- 1 ⁄2 1953

Source: The Falk Corporation.

GEARS AND GEARBOXES

A gear is a form of disc, or wheel, that has teeth around its periphery for the purpose of providing a positive drive by meshing the teeth with similar teeth on another gear or rack

The spur gear might be called the basic gear since all other types have been developed from it Its teeth are straight and parallel to the center bore line, as shown in Figure 11.1 Spur gears may run together with other spur gears or parallel shafts, with internal gears on parallel shafts, and with a rack A rack such as the one illustrated in Figure 11.2 is in effect a straight-line gear The smallest of a pair of gears (Figure 11.3) is often called a pinion

The involute profile or form is the one most commonly used for gear teeth It is a curve that is traced by a point on the end of a taut line unwinding from a circle The larger the circle, the straighter the curvature; for a rack, which is essentially a section of an infinitely large gear, the form is straight or flat The generation of

an involute curve is illustrated in Figure 11.4

The involute system of spur gearing is based on a rack having straight, or flat, sides All gears made to run correctly with this rack will run with each other The sides of each tooth incline toward the center top at an angle called the pressure angle, shown in Figure 11.5

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, and today,

201

Figure 11.1 Example of a spur gear.

Figure 11.2 Rack or straight-line gear

Figure 11.3 Typical spur gears

14.5-degree gearing is generally limited to replacement work The principal reasons are that a 20-degree pressure angle results in a gear tooth with greater strength and wear resistance and permits the use of pinions with a few fewer teeth The effect of the pressure angle on the tooth of a rack is shown in Figure 11.6

It is extremely important that the pressure angle be known when gears are mated,

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 the line tangent to the

Figure 11.4 Invlute curve

Figure 11.5 Pressure angle

pitch circles of mating gears Figure 11.7 illustrates the relationship of the pressure 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 when two standard gears are in correct mesh The diameters of these circles are 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 two pitch diam-eters, as shown in Figure 11.8

This relationship may also be stated in an equation and may be simplified by using 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

C ¼D1þ D2

Example: The center distance can be found if the pitch diameters are known (Figure 11.9)

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 the pitch line or circle,

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

Figure 11.8 Pitch diameter and center distance

Figure 11.9 Determining center distance

DIAMETRICALPITCH ANDMEASUREMENT

The diametrical pitch system is the most widely used, as practically all common-sized gears are made to diametrical pitch dimensions It designates the size and proportions of gear teeth by specifying the number of teeth in the gear for each inch 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 number also 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

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

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

Figure 11.11 illustrates that the diametrical pitch number specifying the number 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 and specifically 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 easily made along it In Figure 11.12, it is clearly shown that there are 10 teeth in 3.1416 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 a gear 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 the mechanic to determine the diametrical pitch of a gear This may be done very easily without the use of precision measuring tools, templates, or gauges Meas-urements need not be exact because diametrical pitch numbers are usually whole numbers Therefore, if an approximate calculation results in a value close to a whole number, that whole number is the diametrical pitch number of the gear

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

Figure 11.12 Number of teeth in 3.1416 in

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

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 the closest fractional size 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 decimal pitch gear

METHOD2

Count the number of teeth in the gear and divide this number by the measured pitch diameter The pitch diameter of the gear is measured from the root or bottom 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 from the 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 also indicates that the gear is a 10 decimal pitch gear

PITCHCALCULATIONS

Diametrical pitch, usually a whole number, denotes the ratio of the number of teeth to a gear’s pitch diameter Stated another way, it specifies the number of teeth 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 the outside diameter of the gear is measured

diameter, diametrical pitch, and number of teeth can be stated mathematically as follows

P¼N

where,

D¼ Pitch diameter

P¼ Diametrical pitch

N¼ Number of teeth

If any two values are known, the third may be found by substituting the known values in the appropriate equation

Example 1: What is the diametrical pitch of a 40-tooth gear with a 5-in pitch diameter?

P¼N

D or P¼40

5 or P¼ 8 diametrical pitch Example 2: What is the pitch diameter of a 12 diametrical pitch gear with 36 teeth?

P or D¼36

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

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

N¼ D  P or N ¼ 3
3=4  16 or N ¼ 60 teeth

Circular pitch is the distance from a point on a gear tooth to the corresponding 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 of teeth in the gear The relationship of the circular pitch to the pitch-circle circumference, number of teeth, and the pitch diameter may also be stated mathematically as follows:

Circumference of pitch circle¼ pD

P¼
D

P where,

D¼ Pitch diameter

N¼ Number of teeth

P ¼ Circular pitch

¼ pi, or 3:1416

If any two values are known, the third may be found by substituting the known values in the appropriate equation

Example 1: What is the circular pitch of a gear with 48 teeth and a pitch diameter

of 6 in.?

P¼
D

N or

3:1416 6

3:1416

8 or P¼ :3927 inches Example 2: What is the pitch diameter of a 0.500-in circular-pitch gear with 128 teeth?

D¼PN

p or

:5 128 3:1416 D¼ 20:371 inches The 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 pitch line or circle

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