Maintenance Fundamentals 2011 Part 8 pot

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. 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 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. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 204 204 Maintenance Fundamentals C ¼ Center distance D 1 ¼ First pitch diameter D 2 ¼ Second pitch diameter C ¼ D 1 þ D 2 2 D 1 ¼ 2C ÀD 2 D 2 ¼ 2C ÀD 1 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. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 205 Gears and Gearboxes 205 DIAMETRICAL PITCH AND MEASUREMENT 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. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 206 206 Maintenance Fundamentals 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. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 207 Gears and Gearboxes 207 METHOD 1 Count the number of teeth in the gear, add 2 to this number, and divide by the outside diameterof thegear. Scalemeasurement of the gear to the closest fractional size is adequate accuracy. Figure 11.14 illustrates a gear with 56 teeth and an outside measurement of 5 ⁄ 13 16 in. 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 decimal pitch gear. METHOD 2 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. PITCH CALCULATIONS 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. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 208 208 Maintenance Fundamentals diameter, diametrical pitch, and number of teeth can be stated mathematically as follows. P ¼ N D D ¼ N P N ¼ D ÂP where, D ¼ Pitch diameter P ¼ Diametrical pitch N ¼ 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? P ¼ N D or P ¼ 40 5 or P ¼ 8 diametrical pitch Example 2: What is the pitch diameter of a 12 diametrical pitch gear with 36 teeth? D ¼ N P or D ¼ 36 12 or D ¼ 3-in: pitch diameter Example 3: How many teeth are there in a 16 diametrical pitch gear with a pitch diameter of 3– 3 ⁄ 4 in.? Figure 11.15 Use of Method 2 to approximate the diametrical pitch. This method uses the pitch diameter of the gear. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 209 Gears and Gearboxes 209 N ¼ D ÂP or N ¼ 3 À 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 circle ¼ pD P ¼ D N D ¼ PN  N ¼ pD P where, D ¼ Pitch diameter N ¼ 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.? P ¼ D N or 3:1416 Â6 48 or 3:1416 8 or P ¼ :3927 inches Example 2: What is the pitch diameter of a 0.500-in. circular-pitch gear with 128 teeth? D ¼ PN p or :5 Â128 3:1416 D ¼ 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. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 210 210 Maintenance Fundamentals  Clearance: Amount by which the dedendum of a gear tooth exceeds the addendum 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 full-depth involute system is the gear system in most common use. The formulas (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. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 211 Gears and Gearboxes 211 Addendum, a ¼ 1 P Whole Depth, W d ¼ 2:0 þ:002 P (20P or smaller) Dedendum, W d ¼ 2:157 P (Larger than 20P) Whole Depth, b ¼ Wd À a Clearance, c ¼ b À a Tooth Thickness, t ¼ 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 spaces exceeds the thickness of the mating gear teeth. Backlash may also be described as the distance, measured along the pitch line, that a gear will move when engaged with another gear that is fixed or immovable, as illustrated in Figure 11.18. Normally there must be some backlash present in gear drives to provide running clearance. This is necessary because binding of mating gears can result in heat generation, noise, abnormal wear, possible overload, and/or failure of the drive. A small amount of backlash is also desirable because of the dimensional vari- ations involved in practical manufacturing tolerances. Backlash is built into standard gears during manufacture by cutting the gear teeth thinner than normal by an amount equal to one half the required figure. When two gears made in this manner are run together, at standard center distance, their allowances combine, provided the full amount of backlash is required. Figure 11.18 Backlash. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 212 212 Maintenance Fundamentals On non-reversing drives or drives with continuous load in one direction, the increase in backlash that results from tooth wear does not adversely affect operation. 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 design and manufacture. Only a general description and explanation of principles will be given, 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 and maintenance work. BEVEL AND MITER Two major differences between bevel gears and spur gears are their shape and the relation of the shafts on which they are mounted. The shape of a spur 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 bevel gears transmit motion between angular or intersecting shafts. The diagram in Figure 11.19 illustrates the bevel gear’s basic cone shape. Figure 11.20 shows a typical pair of bevel gears. Special bevel gears can be manufactured to operate at any desired shaft angle, as shown in Figure 11.21. 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 11.22. A typical pair of straight miter gears is shown in Figure 11.23. Another style of miter gears having spiral rather than straight teeth is shown in Figure 11.24. The spiral-tooth style will be discussed later. 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 the largest. Because each gear in a set of bevel gears must have the same angles and tooth lengths, as well as the same diametrical pitch, they are manufactured and distributed only in mating pairs. Bevel gears, like spur gears, are manufactured in both the 14.5-degree and 20-degree pressure-angle designs. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 213 Gears and Gearboxes 213 [...]... shown in Figure 11. 28 WORM The worm and worm gear, illustrated in Figure 11.29, are used to transmit motion 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 Gears and Gearboxes Figure 11.24 Miter gears with spiral teeth Figure 11.25 Typical set of helical gears 217 2 18 Maintenance Fundamentals Figure... illustrates a typical wear pattern on gears caused by this failure mode 230 Maintenance Fundamentals Figure 11.37 Pattern caused by corrosive attack on gear teeth Figure 11. 38 Pitting caused by gear overloading Overloading The wear patterns generated by excessive gear loading vary, but all share similar components Figure 11. 38 illustrates pitting caused by excessive torsional loading The pits are created...    Overload    Process Induced Misalignment         Worn Bearings   Worn Coupling  Unstable Foundation Water or Chemicals in Gearbox Source: Integrated Systems, Inc      2 28 Maintenance Fundamentals Gear overload is another leading cause of failure In some instances, the overload is constant, which is an indication that the gearbox is not suitable for the application In other cases,... developed It consists simply of two sets of gear teeth, one right hand and one left hand, on the same gear The gear teeth of both hands cause the thrust of one set to cancel out the thrust of 220 Maintenance Fundamentals Figure 11.30 Herringbone gear the other Thus the advantage of helical gears is obtained, and quiet, smooth operation at higher speeds is possible Obviously they can only be used for... power to the mold oscillator system on a continuous caster drives two eccentrics The eccentric rotation of these two cams is transmitted directly into the gearbox and will create the appearance of Maintenance Fundamentals AMPLITUDE GEARMESH 222 FREQUENCY Figure 11.31 Normal profile is symmetrical eccentric meshing of the gears The spacing and amplitude of the gear mesh profile will be destroyed by this... far apart, the teeth will mesh above the pitch line This type of meshing will increase the clearance between teeth and amplify the energy of the actual gear mesh frequency and all of its side bands In addition, the loadbearing characteristics of the gear teeth will be greatly reduced Since the pressure is focused on the tip of each tooth, there is less cross-section and strength in the teeth The potential... non-symmetrical amplitude that represents this disproportional clearance and impact energy CRACKED OR BROKEN TOOTH FREQUENCY Figure 11.33 A broken tooth will produce an asymmetrical side band profile 224 Maintenance Fundamentals If the gear set develops problems, the amplitude of the gear mesh frequency will increase and the symmetry of the side bands will change The pattern illustrated In Figure 11.34 is typical... Helical gears also have a preload by design; the critical force to be considered, however, is the thrust load (axial) generated in normal operation; see Figure 11.12 TF ¼ 126, 000 à HP Dp à RPM 226 Maintenance Fundamentals STF ¼ TF à tan f cos l TTF ¼ TF à tan l where TF ¼ Tangential Force STF ¼ Separating Force TTF ¼ Thrust Force HP ¼ Input horsepower to pinion or gear ¼ Pitch diameter of pinion or gear... either side of the gear’s centerline 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 216 Maintenance Fundamentals Figure 11.23 Typical set of miter gears of how viewed Figure 11.27 illustrates a helical gear as viewed from opposite sides; changing the position of the gear cannot change the hand... suggests one or more potential failure modes for the gearbox Gears and Gearboxes 229 Figure 11.35 Normal wear pattern Figure 11.36 Wear pattern caused by abrasives in lubricating oil Abrasion Abrasion creates unique wear patterns on the teeth The pattern varies, depending on the type of abrasion and its specific forcing function Figure 11.36 illustrates severe abrasive wear caused by particulates in the . side the gear is viewed. Figure 11. 28 Typical set of spiral gears. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 2 18 2 18 Maintenance Fundamentals Figure 11.29 Typical. the outside diameter of the gear is measured. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 2 08 2 08 Maintenance Fundamentals diameter, diametrical pitch, and number of. amount of backlash is required. Figure 11. 18 Backlash. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 212 212 Maintenance Fundamentals On non-reversing drives or drives