Machinery's Handbook, 31st Edition
HELICAL GEARING 2289 In this formula, R d represents the ratio obtained with available gears. If the given lead is 44.0894 inches, as in the preceding example, then the desired ratio as obtained with Formula (5) would be 0.9185292 if K = 1. Assume that the lead gears selected by using logs of ratios have a ratio of 0.9184704; then this ratio error of 0.0000588 would result in a computed lead error of only 0.000065 inch per inch. Formula (5), as mentioned, applies to machines having the differential located ahead of the index gears. If the differential is located after the index gears, it is necessary to change lead gears whenever the index gears are changed for hobbing a different number of teeth, as indicated by the following formula which gives the lead gear ratio. In this formula, D = pitch diameter. (6) General Remarks on Helical Gear Hobbing.— In cutting teeth having large angles, it is desirable to have the direction of helix of the hob the same as the direction of helix of the gear, or in other words, the gear and the hob of the same “hand.” Then the direction of the cut will come against the movement of the blank. At ordinary angles, however, one hob will cut both right- and left-hand gears. In setting up the hobbing machine for helical gears, care should be taken to see that the vertical feed does not trip until the machine has been stopped or the hob has fed down past the finished gear. Herringbone Gears Double helical or herringbone gears are commonly used in parallel-shaft transmissions, especially when a smooth, continuous action (due to the gradual overlapping engagement of the teeth) is essential, as in high-speed drives where the pitch-line velocity may range from about 1000 to 3000 feet per minute(305–914 m/min) in commercial gearing and up to 12,000 feet per minute(3658 m/min) or higher in more specialized installations. These relatively high speeds are encountered in marine reduction gears, in certain speed- reducing and speed-increasing units, and in various other transmissions, particularly in connection with steam turbine and electric motor drives. General Classes of Helical Gear Problems.— There are two general classes of problems. In one, the problem is to design gears capable of transmitting a given amount of power at a given speed, safely and without excessive wear; hence, the required proportions must be determined. In the second, the proportions and speed are known and the power- transmitting capacity is required. The first is the more difficult and common problem. Causes of Herringbone Gear Failures.— Where failure occurs in a herringbone gear transmission, it is rarely due to tooth breakage but usually to excessive wear or sub- surface failures, such as pitting and spalling; hence, it is common practice to base the design of such gears upon durability, or upon tooth pressures which are within the allow- able limits for wear. In this connection, it seems to have been well established by tests of both spur gears and herringbone gears, that there is a critical surface pressure value for teeth having given physical properties and coefficient of friction. According to these tests, pressures above the critical value result in rapid wear and a short gear life, whereas when pressures are below the critical, wear is negligible. The yield point or endurance limit of the material marks the critical loading point, and in practical designing a reasonable fac- tor of safety would, of course, be employed. tan K A D T # # # π R K d # = L T Driving gear sizes Driven gear sizes = =
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