Volume 16 - Machining Part 13 doc

progressive, with two or more teeth sharing the load at the same time. Because they have equal right-hand and left-hand helixes, end thrust is eliminated. Herringbone gears can be operated at higher pitch-line velocities than spur gears. Fig. 5 A typical one-piece herringbone gear. The opposed helixes permit multiple- tooth engagement and eliminate end thrust Crossed-axes helical gears (Fig. 6) operate with shafts that are nonparallel and nonintersecting. Crossed-helical gears are essentially nonenveloping worm gears, that is, both members are cylindrical. The action between mating teeth has a wedging effect, which results in sliding on tooth flanks. These gears have low load-carrying capacity, but are useful where shafts must rotate at an angle to each other. Fig. 6 Mating crossed-axes helical gears Worm gear sets are usually right-angle drives consisting of a worm gear (or worm wheel) and a worm. A single- enveloping worm gear set has a cylindrical worm, but the gear is throated (that is, the gear blank has a smaller diameter in the center than at the ends of the cylinder, the concave shape increasing the area of contact between them) so that it tends to wrap around the worm. In the double-enveloping worm gear set, both members are throated, and both members wrap around each other. A double-enveloping worm gear set is shown in Fig. 7. Worm gear sets are used where the ratio of the speed of the driving member to the speed of the driven member is large, and for a compact right-angle drive. Fig. 7 Mating of worm gear (worm wheel) and worm in a double-enveloping worm gear set Internal gears are used to transmit motion between parallel shafts. Their tooth forms are similar to those of spur and helical gears except that the teeth point inward toward the center of the gear. Common applications for internal gears include rear drives for heavy vehicles, planetary gears, and speed-reducing devices. Internal gears are sometimes used in compact designs because the center distance between the internal gear and its mating pinion is much smaller than that required for two external gears. A typical relation between an internal gear and a mating pinion is shown in Fig. 8. Fig. 8 Section of a spur-type internal gear (a) and relation of internal gear with mating pinion (b) Racks. A rack is a gear having a pitch circle of infinite radius. Its teeth lie along a straight line on a plane. The teeth may be at right angles to the edge of the rack and mesh with a spur gear (Fig. 3b), or the teeth on the rack may be at some other angle and engage a helical gear (Fig. 4b). Bevel gears transmit rotary motion between two nonparallel shafts. These shafts are usually at 90° to each other. Straight bevel gears (Fig. 9a) have straight teeth that, if extended inward, would intersect at the axis of the gear. Thus, the action between mating teeth resembles that of two cones rolling on each other (see Fig. 10 for angles and terminology). The use of straight bevel gears is generally limited to drives that operate at low speeds and where noise is not important. Fig. 9 Four types of bevel gears Fig. 10 Angles and terminology for straight bevel gears Spiral bevel gears (Fig. 9b) have teeth that are curved and oblique. The inclination of the teeth results in gradual engagement and continuous line contact or overlapping action; that is, more than one tooth will be in contact at all times. Because of this continuous engagement, the load is transmitted more smoothly from the driving to the driven gear than with straight bevel gears. Spiral bevel gears also have greater load-carrying capacity than their straight counterparts. Spiral bevel gears are usually preferred to straight bevel gears when speeds are greater than 300 m/min (1000 sfm), and particularly for very small gears. Zerol bevel gears (Fig. 9c) are curved-tooth bevel gears with zero spiral angle. They differ from spiral bevel gears in that the teeth are not oblique. They are used in the same way as spiral bevel gears, and they have somewhat greater tooth strength than straight bevel gears. Hypoid gears (Fig. 9d) are similar to spiral bevel gears in general appearance. The important difference is that the pinion axis of the hypoid pair of gears is offset somewhat from the gear axis. This feature provides many design advantages. In operation, hypoid gears run even more smoothly and quietly than spiral bevel gears and are somewhat stronger. Spiral bevel, Zerol bevel, and hypoid gears are of two types generated and nongenerated. In appearance, the two types are nearly identical, the only difference being a slight variation in the profile shape of the teeth. In a generated pair, the teeth of both the gear and pinion are cut on a generating-type machine, while in a nongenerated pair, only the pinion member is generated, the teeth of the gear being straight-sided. In generating a pinion to operate with a nongenerated gear, the tooth profile is modified to compensate for the lack of profile curvature in the gear tooth. For reasons of tooth design, nongenerated gears are usually limited to ratios of at least 2.5:1. Nongenerated gears are used primarily for economy. Because no generating roll is required when cutting the gear member, machining is several times faster than for a generated counterpart. For this reason, nongenerated bevel gears are widely used when mass production is required. Face gears have teeth cut on the end face of a gear, as the term face gear implies. They are not ordinarily thought of as bevel gears, but functionally they are more akin to bevel gears than to any other type. A spur pinion and a face gear are mounted (like bevel gears) on shafts that intersect and have a shaft angle (usually 90°). The pinion bearings carry mostly radial load, while the gear bearings have both thrust and radial load. The mounting distance of the pinion from the pitch-cone apex is not critical, as it is in bevel or hypoid gears. Figure 11 shows the terminology used with face gears. Fig. 11 Face gear terminology. (a) Cross-sectional view showing gear and pinion positions. (b) Relationsh ip of gear teeth to gear axis The pinion that goes with a face gear is usually made spur, but it can be made helical if necessary. The formulas for determining the dimensions of a pinion to run with a face gear are no different from those for the dimensions of a pinion to run with a mating gear on parallel axes. The pressure angles and pitches used are similar to spur gear (or helical gear) practice. The gear must be finished with a shaper-cutter that is almost the same size as the pinion. Equipment for grinding face gears is not available. The teeth can be lapped, and they can be shaved without too much difficulty, although ordinarily shaving is not used. The face gear tooth changes shape from one end of the tooth to the other. The face width of the gear is limited at the outside end by the radius at which the tooth becomes pointed. At the inside end, the limit is the radius at which undercut becomes excessive. Due to practical considerations, it is usually desirable to make the face width somewhat short of these limits. The pinion to go with a face gear is usually made with a 20° pressure angle. Proper Gear Selection The first step in designing a set of gears is to select the correct type. In many cases, the geometric arrangement of the apparatus that needs a gear drive will considerably affect the selection. If the gears must be on parallel axes, then spur or helical gears are appropriate. Bevel and worm gears can be used if the axes are at right angles, but they are not feasible with parallel axes. If the axes are nonintersecting and nonparallel, then crossed-helical gears, hypoid gears, worm gears, or Spiroid gears can be used. Worm gears, though, are seldom used if the axes are not at right angles to each other. Table 1 lists the principal types of gears and how they are mounted. Table 1 Types of gears in common use Parallel axes • Spur external • Spur internal • Helical external • Helical internal Intersecting axes • Straight bevel • Zerol bevel • Spiral bevel • Face gear Nonintersecting and nonparallel axes • Crossed helical • Single-enveloping worm • Double-enveloping worm • Hypoid • Spiroid There are no dogmatic rules that tell the designer which gear to use. The choice is often made after weighing the advantages and disadvantages of two or three types of gears. Some generalizations, though, can be made about gear selection. External helical gears are generally used when both high speeds and high horsepowers are involved. External helical gears have been built to carry as much as 45,000 kW (60,000 hp) of power on a single pinion and gear. Larger helical gears could also be designed and built. It is doubtful if any other type of gear could be built and used successfully to carry this much power on a single mesh. Bevel gears are ordinarily used on right-angle drives when high efficiency is needed. These gears can usually be designed to operate with 98% or better efficiency. Worm gears seldom operate at efficiencies above 90%. Hypoid gears do not have as good efficiency as bevel gears, but hypoid gears can carry more power in the same space, provided the speeds are not too high. Worm gears are ordinarily used on right-angle drives when very high ratios (single-thread worm and gear) are needed. They are also widely used in low-to-medium ratios (multiple-thread worm and gear) as packaged speed reducers. Single- thread worms and worm gears are used to provide the mechanical indexing accuracy on many machine tools. The critical function of indexing hobbing machines and gear shapers is nearly always done by worm gear drive. Spur gears are relatively simple in design and in the machinery used to manufacture and check them. Most designers prefer to use them wherever design requirements permit. Spur gears are ordinarily thought of as slow-speed gears, while helical gears are thought of as high-speed gears. If noise is not a serious design problem, spur gears can be used at almost any speed that can be handled by other types of gears. Aircraft gas-turbine precision spur gears sometimes operate at pitch-line speeds above 50 m/s (10,000 sfm). In general, though, spur gears are not used much above 20 m/s (4000 sfm). Machining Processes for Gears Simple gear tooth configurations can be produced by basic processes such as milling, broaching, and form tooling. Complex gear tooth configurations require more sophisticated processes designed especially for the manufacture of gears. Processes for Gears Other Than Bevel Gears The methods used to cut the teeth of gears other than bevel gears are milling, broaching, shear cutting, hobbing, shaping, and rack cutting. In any method, a fixture must hold the gear blank in correct relation to the cutter, and the setup must be rigid. Milling produces gear teeth by means of a form cutter. The usual practice is to mill one tooth space at a time. After each space is milled, the gear blank is indexed to the next cutting position. Peripheral milling can be used for the roughing of teeth in spur and helical gears. Figure 12 shows teeth in a spur gear being cut by peripheral milling with a form cutter. End milling can also be used for cutting teeth in spur or helical gears and is often used for cutting coarse-pitch teeth in herringbone gears. Fig. 12 Relation of cutter and workpiece when milling teeth in a spur gear In practice, gear milling is usually confined to one-of-a-kind replacement gears, small-lot production, the roughing and finishing of coarse-pitch gears, and the finish milling of gears having special tooth forms. Although high-quality gears can be produced by milling, the accuracy of tooth spacing on older gear milling machines was limited by the inherent accuracy of the indexing mechanism. Most indexing techniques used on modern gear milling machines incorporate numerical control or computer numerical control, and the accuracy can rival that of hobbing machines. Broaching. Both external and internal gear teeth, spur or helical, can be broached, but conventional broaching is usually confined to cutting teeth in internal gears. Figure 13 shows progressive broach steps in cutting an internal spur gear. The form of the space between broached gear teeth corresponds to the form of the broach teeth. The cutting action of any single broach tooth is similar to that of a single form tool. Each cross section of the broach has as many teeth as there are tooth spaces on the gear. The diameter of each section increases progressively to the major diameter that completes the tooth form on the workpiece. Broaching is fast, and accurate, but the cost of tooling is high. Therefore, broaching of gear teeth is best suited to large production runs. Fig. 13 Progressive action of broach teeth in cutting teeth of an internal spur gear Shear cutting is a high-production method for producing teeth in external spur gears. The process is not applicable to helical gears. In shear cutting, as in broaching, all tooth spaces are cut simultaneously and progressively (Fig. 14). Cutting speeds in shear cutting are similar to those for broaching the same work metal. Machines are available for cutting gears up to 508 mm (20 in.) in diameter, with face width up to 152 mm (6 in.). Fig. 14 Progressive action in shea r cutting teeth of an external spur gear. Shear cutting operation proceeds from roughing (a) to intermediate (b) to finishing (c) operations The shear cutting head is mounted in a fixed position, and the gear blanks are pushed through the head. Cutting tools are fed radially into the head, a predetermined amount for each stroke, until the required depth of tooth space is reached. In shear cutting, some space is required for over-travel, although most workpieces with integral shoulders or flanges (such as cluster gears) do have enough clearance between sections to allow shear cutting to be used. Therefore, this process is best suited to large production runs. Hobbing is a practical method for cutting teeth in spur gears, helical gears, worms, worm gears, and many special forms. Conventional hobbing machines are not applicable to cutting bevel and internal gears. Tooling costs for hobbing are lower than those for broaching or shear cutting. Therefore, bobbing is used in low-quantity production or even for a few pieces. On the other hand, hobbing is a fast and accurate method (compared to milling, for example) and is therefore suitable for medium and high production quantities. Hobbing is a generating process in which both the cutting tool and the workpiece revolve in a constant relation as the hob is being fed across the face width of the gear blank. The hob is a fluted worm with form-relieved teeth that cut into the gear blank in succession, each in a slightly different position. Instead of being formed in one profile cut, as in milling, the gear teeth are generated progressively by a series of cuts (Fig. 15). The hobbing of a spur gear is shown in Fig. 16. Fig. 15 Schematic of hobbing action. Gear tooth is generated progressively by hob teeth. Fig. 16 Hobbing of a spur gear Gear shaping is the most versatile of all gear cutting processes. Although shaping is most commonly used for cutting teeth in spur and helical gears, this process is also applicable to cutting herringbone teeth, internal gear teeth (or splines), chain sprockets, ratchets, elliptical gears, face gears, worm gears, and racks. Shaping cannot be used to cut teeth in bevel gears. Because tooling costs are relatively low, shaping is practical for any quantity of production. Workpiece design [...]... 95 100 135 S5, S11 M3, M42 15 0-2 00 Hot rolled, normalized, annealed, or cold drawn 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and finer 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and finer 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and 1.50 1.50 1.50 1.25 0.75 Quenched and tempered 2 5-1 3 1 2-2 .5 2-1 .5 1-0 .5 0.5 and finer 2 5-1 3 1 2-2 .5 2-1 .5 1-0 .5 0.5 and finer 2 5-1 3 1 2-2 .5 2-1 .5 1-0 .5 0.5 and 2 1 1 1 1 32 5-3 75 Wrought free -machining alloy steels Medium-carbon... 2-1 .5 1-0 .5 0.5 and finer 2 5-1 3 1 2-2 .5 2-1 .5 1-0 .5 0.5 and finer 2 5-1 3 1 2-2 .5 2-1 .5 1-0 .5 0.5 and finer 2 5-1 3 1 2-2 .5 2-1 .5 1-0 .5 0.5 and finer 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and finer 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and finer 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and finer 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and finer 2 1 1 1 1 1.15 1.15 1.15 1.15 0.75 0.045 0.045 0.045 0.045 0.030 21 27 34 37 40 70 90 110 120 130 S5, S11 M3, M42 2 1 1 1 1 1.50... 70 90 110 120 130 S5, S11 M3, M42 2 1 1 1 1 1.65 1.65 1.50 1.25 0.75 0.065 0.065 0.060 0.050 0.030 78 81 90 95 105 255 265 295 305 340 S4, S2 M2, M7 2 1.50 0.060 50 165 S4, M2, Diametral pitch 2 5-1 3 1 2-2 .5 2-1 .5 1-0 .5 0.5 and finer 2 5-1 3 1 2-2 .5 2-1 .5 1-0 .5 0.5 and finer 2 5-1 3 1 2-2 .5 2-1 .5 1-0 .5 0.5 and finer 2 5-1 3 1 2-2 .5 2-1 .5 1-0 .5 0.5 and finer 2 5-1 3 1 2-2 .5 2-1 .5 1-0 .5 0.5 and finer 2 5-1 3 Number of... 12L13, 12L14, 12L15 17 5-2 25 32 5-3 75 Medium-carbon resulfurized: 1132 , 1137 , 1139 , 1140, 1141, 1144, 1145, 1146, 1151 Cold drawn Annealed or cold drawn 12 5-1 75 Hot rolled, normalized, annealed, or cold drawn 32 5-3 75 Quenched and tempered Diametral pitch 2 5-6 5-3 2-1 .5 1 and finer 2 5-6 5-3 2-1 .5 1 and finer 2 5-6 5-3 2-1 .5 1 and finer 2 5-6 5-3 2-1 .5 1 and finer 2 5-6 5-3 2-1 .5 1 and finer 2 5-6 5-3 2-1 .5... 86L40 15 0-2 00 Quenched and tempered 12 5-1 75 Hot rolled, annealed, or cold drawn 32 5-3 75 Normalized or quenched and tempered 17 5-2 25 Hot rolled, annealed, or cold drawn 32 5-3 75 Normalized or quenched and tempered finer 2 5-6 5-3 2-1 .5 1 and finer 2 5-6 5-3 2-1 .5 1 and finer 2 5-6 5-3 2-1 .5 1 and finer 2 5-6 5-3 2-1 .5 1 and finer 1-4 5-1 0 1 1-1 9 20 and finer 1-4 5-1 0 1 1-1 9 20 and finer 1-4 5-1 0 1 1-1 9 20 and... S2 M2, M7 2 5-6 5-3 2-1 .5 1 and finer 2 5-6 5-3 2-1 .5 1 and finer 2 5-6 5-3 2-1 .5 1 and finer 2 5-6 5-3 2-1 .5 1 and 1-4 5-1 0 1 1-1 9 20 and finer 1-4 5-1 0 1 1-1 9 20 and finer 1-4 5-1 0 1 1-1 9 20 and finer 1-4 5-1 0 1 1-1 9 20 and 0.3 0.2 0.12 0.07 0.012 0.008 0.005 0.003 160 525 S4, S2 M2, M7 0.3 0.2 0.12 0.07 0.012 0.008 0.005 0.003 115 375 S4, S2 M2, M7 0.3 0.2 0.12 0.07 0.012 0.008 0.005 0.003 135 450 S4, S2... 12 5-1 75 Hot rolled, normalized, annealed, or cold drawn 2 1 1 1 1 1.80 1.80 1.50 1.25 0.75 0.070 0.070 0.060 0.050 0.030 50 53 56 60 64 165 175 185 200 210 S4, S2 M2, M7 Quenched and tempered 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and finer 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and finer 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and finer 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and finer 2 1 1 1 1 Annealed or cold drawn 2 5-1 3 1 2-2 .5 2-1 .5 1-0 .5 0.5 and finer 2 5-1 3... tempered 10 0-1 50 Hot rolled, normalized, annealed, or cold drawn 20 0-2 50 Hot rolled, 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and finer 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and finer 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and finer 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and finer 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and finer 1-2 Feed per revolution of workpiece(a) mm in Hob speed High-speed steel tool material m/min sfm ISO AISI 2 1 1 1 1 1.50 1.50 1.50 1.25 0.75 0.060... and finer 1-4 5-1 0 1 1-1 9 20 and finer 0.3 0.2 0.12 0.07 0.012 0.008 0.005 0.003 150 500 S4, S2 M2, M7 0.3 0.2 0.12 0.07 0.012 0.008 0.005 0.003 76 250 S5 M3 0.3 0.2 0.12 0.07 0.012 0.008 0.005 0.003 160 525 S4, S2 M2, M7 0.3 0.2 0.12 0.07 0.012 0.008 0.005 0.003 84 275 S5 M3 2 5-6 5-3 2-1 .5 1 and finer 2 5-6 5-3 2-1 .5 1 and finer 2 5-6 5-3 2-1 .5 1 and finer 2 5-6 5-3 2-1 .5 1 and finer 1-4 5-1 0 1 1-1 9 20 and... 12 5-1 75 27 5-3 25 Wrought alloy steels Low carbon: 4012, 4023, 4024, 4118, 4320, 4419, 4422, 4615, 4617, 4620, 4621, 4718, 4720, 4815, 4817, 4820, 5015, 5115, 5120, 6118, 8115, 8617, 8620, 8622, 8822, 9310, 94B15, 94B17 Quenched and tempered Normalized or quenched and temper finer 2 5-1 3 1 2-2 .5 2-1 .5 1-0 .5 0.5 and finer finer 1-2 3-1 0 1 1-1 9 2 0-4 8 48 and finer 2 5-1 3 1 2-2 .5 2-1 .5 1-0 .5 0.5 and finer 2 5-1 3 . are ordinarily used on right-angle drives when very high ratios (single-thread worm and gear) are needed. They are also widely used in low-to-medium ratios (multiple-thread worm and gear) as packaged. have end- cutting or bottom-cutting blades alternately spaced with inside and outside blades. There are four basic cutting methods:completing, single-side, fixed-setting, and single-setting cutting coarse-pitch teeth in herringbone gears. Fig. 12 Relation of cutter and workpiece when milling teeth in a spur gear In practice, gear milling is usually confined to one-of-a-kind replacement