Industrial Machinery Repair Part Episode 2 Part 3 potx

284 Gears and Gearboxes 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, and today 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 fewer teeth. The effect of the pressure angle on the tooth of a rack is shown in Figure 14.6. Gears and Gearboxes 285 Cord x Base circle Figure 14.4 Involute curve Pressure an g le Figure 14.5 Pressure angle 14½° 20 ° Figure 14.6 Different pressure angles on gear teeth 286 Gears and Gearboxes Pressure angle Pressure angle Direction of tooth to tooth push Rotation Line of action 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 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 pitch circles of mating gears. Figure 14.7 illustrates the relationship 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 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 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 Gears and Gearboxes 287 Center distance Pitch dia. Pitch dia. Figure 14.8 Pitch diameter and center distance Center distance (C) 4" Pitch dia. 8½" Pitch dia. Figure 14.9 Determining center distance D 1 = first pitch diameter D 2 = second pitch diameter C = D 1 + D 2 2 D 1 = 2C −D 2 D 2 = 2C −D 1 Example: The center distance can be found if the pitch diameters are known (illustration in Figure 14.9). 288 Gears and Gearboxes 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 the pitch line or circle, as illustrated in Figure 14.10. Large-diameter gears are frequently made to circular pitch dimensions. Diametrical Pitch and Measurement The diametrical pitch system is the most widely used, as practically all common-size 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 (π) inches, or 3.1416 inches, of pitch-circle circumfer- ence. The diametric pitch number also designates the number of teeth for each 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 the diametrical pitch number specifying the number of teeth per inch of pitch diameter must also specify the number of teeth 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. Gears and Gearboxes 289 3.1416 " 3.1416" 3.1416" 3.1416 " 1" 1" 1" 1" Figure 14.11 Pitch diameter and diametrical pitch 3.1416" 12345678 910 Figure 14.12 Number of teeth in 3.1416 inches Because the pitch line of a rack is a straight line, a measurement can be easily made along it. In Figure 14.12, it is clearly shown that there are 10 teeth in 3.1416 inches; therefore the rack illustrated is a 10 diametrical pitch rack. 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 of pitch line, the gear in this illustration is also a 10 diametrical pitch gear. In many cases, particularly on 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. Measurements need not be exact because diametrical pitch numbers 290 Gears and Gearboxes 3.1416" 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 diametrical pitch number of the gear. The following two methods may be used to determine the approximate dia- metrical pitch of a gear. A common steel rule, preferably flexible, is adequate 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 the closest fractional size is adequate accuracy. Figure 14.14 illustrates a gear with 56 teeth and an outside measurement of 5 13 16 inches. Adding 2 to 56 gives 58; dividing 58 by 5 13 16 gives an answer of 9 31 32 . 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 mea- sured 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 14.15 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 inches. Dividing 56 by 5 5 8 gives an answer of 9 15 16 inches, or approximately 10. This method also indicates that the gear is a 10 diametrical pitch gear. Gears and Gearboxes 291 5 13/16" Figure 14.14 Using method 1 to approximate the diametrical pitch. In this method the outside diameter of the gear is measured. 5 5/8" Figure 14.15 Using method 2 to approximate the diametrical pitch. This method uses the pitch diameter of the gear. Pitch Calculations Diametrical pitch, usually a whole number, denotes the ratio of the num- ber 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 relation- ship of pitch diameter, diametrical pitch, and number of teeth can be stated mathematically as follows. P = N D D = N P N = D × P 292 Gears and Gearboxes Where: D = pitch diameter P = diametrical pitch N = 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-inch pitch diameter? P = N P or P = 40 5 or P = 8 diametrical pitch Example 2: What is the pitch diameter of a 12 diametrical pitch gear with 36 teeth? D = N P or D = 36 12 or D = 3" pitch diameter Example 3: How many teeth are there in a 16 diametrical pitch gear with a pitch diameter of 3 3 4 inches? N = D × PorN= 3 3 4 × 16 or N = 60 teeth Circular 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 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 circle = π D p = πD N D = pN π N = πD p Where: D = pitch diameter N = number of teeth p = circular pitch π = pi, or 3.1416 If any two values are known, the third may be found by substituting the known values in the appropriate equation. Gears and Gearboxes 293 Example 1: What is the circular pitch of a gear with 48 teeth and a pitch diameter of 6"? p = πD N or 3.1416 ×6 48 or 3.1416 8 or p = .3927 inches Example 2: What is the pitch diameter of a .500" circular-pitch gear with 128 teeth? D = pN π or .5 ×128 3. 1416 D = 20.371 inches The list that follows offers just a few names of the various parts given to gears. These parts are shown in Figures 14.16 and 14.17. ● Addendum: Distance the tooth projects above, or outside, the pitch line or circle. Clearance Working depth Thickness Dedendum Addendum Circular pitch Pitch circle Whole depth Pitch circle Figure 14.16 Names of gear parts Pitch line Thickness Addendum Dedendum Whole depth Circular pitch Figure 14.17 Names of rack parts [...]... defect that may be present If the shafts are too far apart, the teeth will mesh above the pitch line This type of meshing will increase the clearance between teeth and amplify the AMPLITUDE 19 Hz 1x INPUT 16 Hz 20 Hz FREQUENCY Figure 14. 32 Wear or excessive clearance changes sideband spacing AMPLITUDE 30 6 Gears and Gearboxes FREQUENCY Figure 14 .33 A broken tooth will produce an asymmetrical sideband... teeth A disadvantage, however, is the higher friction and wear that accompanies 29 8 Gears and Gearboxes 90° 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 of the... number of starts or entrances at the end of the worm The thread of the Gears and Gearboxes 30 1 Angle Angle Hub on left side Hub on right 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 3 02 Gears and Gearboxes Figure 14 .29 Typical set of worm gears worm is an important feature in worm design, as it is a major... as −1 and +1 in Figure 14 .31 , will be spaced at exactly input speed and have the same amplitude If the gear mesh profile were split by drawing a vertical line through the actual mesh, i.e., the number of teeth times the input shaft speed, the two halves would be exactly identical Any deviation from a symmetrical gear Gear mesh Amplitude Ϫ1 2 3 Ϫ4 ϩ1 2 3 Frequency Figure 14 .31 Normal profile is symmetrical... basic cone shape Figure 14 .20 shows a typical pair of bevel gears Special bevel gears can be manufactured to operate at any desired shaft angle, as shown in Figure 14 .21 Miter gears are bevel gears with the same number 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... (with symbols) shown below are used for calculating tooth proportions of full-depth involute gears Diametrical pitch is given the symbol P as before 1 Addendum, a = P 20 + 0 0 02 (20 P or smaller) Whole depth, Wd = P 2. 157 (larger than 20 P) Dedendum, Wd = P Whole depth, b = Wd − a Clearance, c = b − a Tooth thickness, t = 1 5708 P Backlash Backlash in gears is the play between teeth that prevents binding... 14.19 Basic shape of bevel gears Gears and Gearboxes 29 7 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 -degree pressure-angle designs Helical Helical gears are designed for parallel-shaft operation like the pair in Figure 14 .25 They are similar to spur gears except that the teeth... hand of the helix is the same regardless of how it is viewed Figure 14 .26 illustrates a helical gear as Gears and Gearboxes 29 9 Figure 14 .24 Miter gears with spiral teeth viewed from opposite sides; changing the position of the gear cannot change the hand of the tooth’s helix angle A pair of helical gears, as illustrated in Figure 14 .27 , must have the same pitch and helix angle but must be of opposite... with normal operation Characterization of a gearbox’s Gears and Gearboxes 30 3 Figure 14 .30 Herringbone gear vibration signature box is difficult to acquire but is an invaluable tool for diagnosing machine-train problems The difficulty is that: (1) it is often difficult to mount the transducer close to the individual gears and (2) the number of vibration sources in a multigear drive results in a complex... “hand.” The hand is determined by the direction of the angle of the teeth Thus, in order for a worm and worm gear to mesh correctly, they must be the same hand 30 0 Gears and Gearboxes Figure 14 .25 Typical set of helical gears Helix angle Figure 14 .26 Illustrating the angle at which the teeth are cut The most commonly used worms have either one, two, three, or four separate threads and are called single, . = πD N or 3. 1416 ×6 48 or 3. 1416 8 or p = .3 927 inches Example 2: What is the pitch diameter of a .500" circular-pitch gear with 128 teeth? D = pN π or .5 × 128 3. 1416 D = 20 .37 1 inches The. diameter D 2 = second pitch diameter C = D 1 + D 2 2 D 1 = 2C −D 2 D 2 = 2C −D 1 Example: The center distance can be found if the pitch diameters are known (illustration in Figure 14.9). 28 8 Gears. 8 diametrical pitch Example 2: What is the pitch diameter of a 12 diametrical pitch gear with 36 teeth? D = N P or D = 36 12 or D = 3& quot; pitch diameter Example 3: How many teeth are there