Maintenance Fundamentals Episode 2 part 1 potx

Hubs H/2 Y Shafts W Y 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 StockWidth Depth 5 ⁄ 16 to 7 ⁄ 16 3 ⁄ 32 3 ⁄ 64 3 ⁄ 32  3 ⁄ 32 1 ⁄ 2 to 9 ⁄ 16 1 ⁄ 8 1 ⁄ 16 1 ⁄ 8  1 ⁄ 8 5 ⁄ 8 to 7 ⁄ 8 3 ⁄ 16 3 ⁄ 32 3 ⁄ 16  3 ⁄ 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 3- 13 ⁄ 16 to 4- 1 ⁄ 2 1 1 ⁄ 2 1  1 *Square keys are normally used through shaft diameter 4- 1 ⁄ 2 in.; larger shafts normally use flat keys. Source: The Falk Corporation. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:35pm page 194 194 Maintenance Fundamentals Y ¼ D À ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D 2 À W 2 p 2 where: C ¼ Allowance or clearance for key, inches D ¼ Nominal shaft or bore diameter, inches Table 10.3 Standard Flat Keys and Keyways (inches) Diameter Of Holes (Inclusive) Keyways Key StockWidth Depth 1 ⁄ 2 to 9 ⁄ 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 ⁄ 16 to 1- 3 ⁄ 8 00 5 ⁄ 16 1 ⁄ 8 5 ⁄ 16  1 ⁄ 4 1- 7 ⁄ 16 to 1- 3 ⁄ 4 00 3 ⁄ 8 1 ⁄ 8 3 ⁄ 8  1 ⁄ 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 ⁄ 16 to 3- 3 ⁄ 4 00 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 1 1 ⁄ 4  7 ⁄ 8 5- 9 ⁄ 16 to 6- 1 ⁄ 2 00 1- 1 ⁄ 2 1 ⁄ 2 1- 1 ⁄ 2  1 6- 9 ⁄ 16 to 7- 1 ⁄ 2 00 1- 3 ⁄ 4 5 ⁄ 8 1- 3 ⁄ 4  1 ⁄ 4 7- 9 ⁄ 16 to 9 00 2 3 ⁄ 4 2  1- 3 ⁄ 4 9- 1 ⁄ 16 to 11 00 2- 1 ⁄ 2 7 ⁄ 8 2- 1 ⁄ 2  1- 3 ⁄ 4 11- 1 ⁄ 16 to 13 00 313 2 13- 1 ⁄ 16 to 15 00 3- 1 ⁄ 2 1- 1 ⁄ 4 3- 1 ⁄ 2  2- 1 ⁄ 2 15- 1 ⁄ 6 to 18 00 41- 1 ⁄ 2 4  3 18- 1 ⁄ 16 to 22 00 51- 3 ⁄ 4 5  3 1 ⁄ 2 22- 1 ⁄ 16 to 26 00 64 26- 1 ⁄ 16 to 30 00 75 Source: The Falk Corporation. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:35pm page 195 Couplings 195 H ¼ Nominal key height, inches W ¼ 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. KEYWAY MANUFACTURING TOLERANCES 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 Keyseat Bore Lead Lead B Figure 10.18 Manufacturing tolerances. A, Offset. B, Lead. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:35pm page 196 196 Maintenance Fundamentals KEY STRESS CALCULATIONS 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): Ss ¼ 2T (d)  (w) Â(L) Sc ¼ 2T (d)  (h 1 ) Â(L) where: d ¼ Shaft diameter, inches (use average diameter for taper shafts) h 1 ¼ Height of key in the shaft or hub that bears against the keyway, inches. Should equal h 2 for square keys. For designs where unequal portions of the key are in the hub or shaft, h 1 is the minimum portion. Hp ¼ Power, horsepower L ¼ Effective length of key, inches RPM ¼ Revolutions per minute Ss ¼ Shear stress, psi Sc ¼ Compressive stress, psi T ¼ Shaft torque, lb-in. or Hp  63000 RPM w ¼ Key width, inches Figure 10.19 Measurements used in calculating shear and compressive key stress. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:35pm page 197 Couplings 197 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 -inch  3 ⁄ 4 -inch key, 4-inch key engagement length. T ¼ Torque ¼ Hp  63; 000 RPM ¼ 300 Â63; 000 600 ¼ 31; 500 in-lbs Ss ¼ 2T d Âw ÂL ¼ 2 Â31; 500 3 Â3=4 Â4 ¼ 7; 000 psi Sc ¼ 2T d Âh 1  L ¼ 2 Â31; 500 3 Â3=8 Â4 ¼ 14; 000 psi The AISI 1018 key can be used since it is within allowable stresses listed in Table 10.4 (allowable Ss ¼ 7,500, allowable Sc ¼ 5,000). Note: If shaft had been 2- 3 ⁄ 4 -in. diameter (4-in. hub), the key would be 5 ⁄ 8 -in.  5 ⁄ 8 -in., Ss ¼ 9,200 psi, Sc ¼ 18,400 psi, and a heat-treated key of AISI 1045 would have been required (allowable Ss ¼ 15,000, allowable Sc ¼ 30,000). SHAFT STRESS CALCULATIONS 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 Diameter ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Hp  321000 RPM ÂAllowable Stress 3 r Table 10.4 Allowable Stresses for AISI 1018 and AISI 1045 Material Heat Treatment Allowable Stresses – psi Shear Compressive AISI 1018 None 7,500 15,000 AISI 1045 255-300 Bhn 15,000 30,000 Source: The Falk Corporation. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:35pm page 198 198 Maintenance Fundamentals Example: Hp ¼ 300 RPM ¼ 30 Material ¼ 225 Brinell From Figure 10.20 at 225 Brinell, Allowable Torsion ¼ 8000 psi Minimum Shaft Diameter ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 300 Â321000 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 Stress ¼ Hp Â321; 000 RPM Âd 3 TENSILE STRENGTH, 1000 PSI (APPROX.) BRINELL HARDNESS 80 160 200 240 280 320 360 400 440 100 120 140 160 180 200 220 20000 16000 12000 8000 24000 4000 ALLOWABLE TENSILE STRENGTH (psi) Bending Torsion Figure 10.20 Allowable stress as a function of Brinell hardness. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:35pm page 199 Couplings 199 Example: Given 7- 1 ⁄ 2 -in. shaft for 300 Hp at 30 RPM Shaft Stress ¼ 300 Â321; 000 30  (7 À 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) DD 3 DD 3 DD 3 1 1.00 5 125.0 9 729 1- 1 ⁄ 4 1.95 5- 1 ⁄ 4 145 9- 1 ⁄ 2 857 1- 1 ⁄ 2 3.38 5- 1 ⁄ 2 166.4 10 1000 1- 3 ⁄ 4 5.36 5- 3 ⁄ 4 190.1 10- 1 ⁄ 2 1157 2 8.00 6 216 11 1331 2- 1 ⁄ 4 11.39 6- 1 ⁄ 4 244 11- 1 ⁄ 2 1520 2- 1 ⁄ 2 15.63 6- 1 ⁄ 2 275 12 1728 2- 3 ⁄ 4 20.80 6- 3 ⁄ 4 308 12- 1 ⁄ 2 1953 3 27.00 7 343 13 2197 3- 1 ⁄ 4 34.33 7- 1 ⁄ 4 381 14 2744 3- 1 ⁄ 2 42.88 7- 1 ⁄ 2 422 15 3375 3- 3 ⁄ 4 52.73 7- 3 ⁄ 4 465 16 4096 4 64.00 8 512 17 4913 4- 1 ⁄ 4 76.77 8- 1 ⁄ 4 562 18 5832 4- 1 ⁄ 2 91.13 8- 1 ⁄ 2 614 19 6859 4- 3 ⁄ 4 107.2 8- 3 ⁄ 4 670 20 8000 Source: The Falk Corporation. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:35pm page 200 200 Maintenance Fundamentals 11 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. SPUR GEARS 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, Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 201 201 Figure 11.1 Example of a spur gear. Figure 11.2 Rack or straight-line gear. Figure 11.3 Typical spur gears. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 202 202 Maintenance Fundamentals 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. Keith Mobley /Maintenance Fundamentals Final Proof 15.6.2004 7:38pm page 203 Gears and Gearboxes 203 [...]... the required measurements Figure 11 . 12 Number of teeth in 3 .14 16 in Figure 11 .13 Number of teeth in 3 .14 16 in on the pitch circle 20 8 Maintenance Fundamentals 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 11 .14 illustrates a gear with 56 teeth... 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 Gears and Gearboxes 21 1 Figure 11 .16 Names of gear parts Figure 11 .17 Names of rack parts     Clearance: Amount by which the... diameters, 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: Gears and Gearboxes 20 5 Figure 11 .8 Pitch diameter and center distance Figure 11 .9 Determining center distance C ¼ Center distance D1 ¼ First pitch diameter D2 ¼ Second pitch diameter D1 þ D2 D1 ¼ 2C À D2 C ¼ 2 D2 ¼ 2C À D1 Example: The center... number of Figure 11 .11 Pitch diameter and diametrical pitch Gears and Gearboxes 20 7 teeth per 3 .14 16 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 .14 16 in.; therefore... or 3 :14 16 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 3 :14 16  6 3 :14 16 or or or P ¼ :3 927 inches N 48 8 Example 2: What is the pitch diameter of a 0.500-in circular-pitch gear with 12 8 teeth? D¼ PN or p :5  12 8 3 :14 16 D ¼ 20 :3 71 inches... inches, or 3 .14 16 in., of pitch-circle circumference The diametric pitch number also designates the number of teeth for each 3 .14 16 in of pitch-circle circumference Stated in another way, the diametrical pitch number specifies the number of teeth in 3 .14 16 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... 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... used for calculating tooth proportions of full-depth involute gears Diametrical pitch is given the symbol P as before  21 2 Maintenance Fundamentals Addendum, a ¼ 1 P 2: 0 þ :0 02 (20 P or smaller) P 2: 15 7 (Larger than 20 P) Dedendum, Wd ¼ P Whole Depth, b ¼ Wd À a Clearance, c ¼ b À a 1: 5708 Tooth Thickness, t ¼ P Whole Depth, Wd ¼ BACKLASH Backlash in gears is the play between teeth that prevents binding... equation Example 1: What is the diametrical pitch of a 40-tooth gear with a 5-in pitch diameter? P¼ N 40 or P ¼ or P ¼ 8 diametrical pitch D 5 Example 2: What is the pitch diameter of a 12 diametrical pitch gear with 36 teeth? D¼ N 36 or D ¼ or D ¼ 3-in: pitch diameter P 12 Example 3: How many teeth are there in a 16 diametrical pitch gear with a pitch diameter of 3–3⁄4 in.? 21 0 Maintenance Fundamentals. .. 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 . Inches) DD 3 DD 3 DD 3 1 1.00 5 12 5 .0 9 729 1- 1 ⁄ 4 1. 95 5- 1 ⁄ 4 14 5 9- 1 ⁄ 2 857 1- 1 ⁄ 2 3.38 5- 1 ⁄ 2 16 6.4 10 10 00 1- 3 ⁄ 4 5.36 5- 3 ⁄ 4 19 0 .1 10- 1 ⁄ 2 11 57 2 8.00 6 21 6 11 13 31 2- 1 ⁄ 4 11 .39 6- 1 ⁄ 4 24 4. 6- 1 ⁄ 4 24 4 11 - 1 ⁄ 2 1 520 2- 1 ⁄ 2 15 .63 6- 1 ⁄ 2 275 12 1 728 2- 3 ⁄ 4 20 .80 6- 3 ⁄ 4 308 12 - 1 ⁄ 2 19 53 3 27 .00 7 343 13 21 97 3- 1 ⁄ 4 34.33 7- 1 ⁄ 4 3 81 14 27 44 3- 1 ⁄ 2 42. 88 7- 1 ⁄ 2 422 15 3375 3- 3 ⁄ 4 52. 73. 7- 1 ⁄ 2 00 1- 3 ⁄ 4 5 ⁄ 8 1- 3 ⁄ 4  1 ⁄ 4 7- 9 ⁄ 16 to 9 00 2 3 ⁄ 4 2  1- 3 ⁄ 4 9- 1 ⁄ 16 to 11 00 2- 1 ⁄ 2 7 ⁄ 8 2- 1 ⁄ 2  1- 3 ⁄ 4 11 - 1 ⁄ 16 to 13 00 313  2 13 - 1 ⁄ 16 to 15 00 3- 1 ⁄ 2 1- 1 ⁄ 4 3- 1 ⁄ 2  2- 1 ⁄ 2 15 - 1 ⁄ 6 to 18 00 41- 1 ⁄ 2 4