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11.7.3 Axial Thrust and Radial Separating Forces The formulas that follow are used to calculate the axial thrust force Wx and the radial separating force WR for bevel and hypoid gears. The direction of the pinion (driver) rotation should be viewed from the pinion back. For a pinion (driver) with a right-hand (RH) spiral with clockwise (cw) rotation or a left-hand (LH) spiral with counterclockwise (ccw) rotation, the axial and separating force components acting on the pinion are, respectively, WxP = WtP sec P (tan sin sin P cos ) WRP = WtP sec P (tan cos + sin P sin ) (11.6) (11.7)
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For a pinion (driver) with an LH spiral with cw rotation or an RH spiral with ccw rotation, the force components acting on the pinion are, respectively, WxP = WtP sec P (tan sin + sin P cos ) WRP = WtP sec P (tan cos sin P sin ) (11.8) (11.9)
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For a pinion (driver) with an RH spiral with cw rotation or an LH spiral with ccw rotation, the force components acting on the gear (driven) are, respectively, WxG = WtG sec G (tan sin + sin G cos ) WRG = WtG sec G (tan cos sin G sin ) (11.10) (11.11)
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For a pinion (driver) with an LH spiral and cw rotation or an RH spiral with ccw rotation, the force components acting on the gear are, respectively, WxG = WtG sec G (tan sin sin G cos ) WRG = WtG sec G (tan cos + sin G sin ) (11.12) (11.13)
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These equations apply to straight-bevel, Zerol bevel, spiral-bevel, and hypoid gears. When you use them for hypoid gears, be sure that the pressure angle corresponds to the driving face of the pinion tooth. A plus sign for Eqs. (11.6), (11.8), (11.10), and (11.12) indicates that the direction of the axial thrust is outward, or away from the cone center. Thus a minus sign indicates that the direction of the axial thrust is inward, or toward the cone center. A plus sign for Eqs. (11.7), (11.9), (11.11), and (11.13) indicates that the direction of the separating force is away from the mating gear. So a minus sign indicates an attracting force toward the mating member. Example. A hypoid-gear set consists of an 11-tooth pinion with LH spiral and ccw rotation driving a 45-tooth gear. Data for the gear are as follows: 4.286 diametral pitch, 8.965-inch (in) mean diameter, 70.03 pitch angle, 31.48 spiral angle, and 30 103 lb in torque. Pinion data are these: 1.500-in offset, 2.905-in mean diameter, concave pressure angle 18.13 , convex pressure angle 21.87 , pitch angle 19.02 , and spiral angle 50 . Determine the force components and their directions for each member of the set. Solution. From Eq. (11.4) we find the tangential load on the gear to be WtG = 2TG 2(30 103) = = 6693 lb Dm 8.965
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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Since the pinion has LH spiral angle and rotates ccw, Eqs. (11.10) and (11.11) apply for the gear. Thus WxG = WtG sec G (tan sin + sin G cos ) = 6693 sec 31.48 (tan 18.13 sin 70.03 + sin 31.48 cos 70.03 ) = 3814 lb Substituting the same values and angles into Eq. (11.11) gives WRG = 2974 lb. Thus the thrust is outward, and the separating force is toward the mating member. Next we find the tangential load on the pinion from Eq. (11.5): WtP = WtG cos P 6693 cos 50 = = 5045 lb cos G cos 31.48
Equations (11.6) and (11.7) apply to the pinion: WxP = WtP sec P (tan sin sin P cos ) = 5045 sec 50 (tan 18.13 sin 19.02 sin 50 cos 19.02 ) = 4846 lb In a similar manner, Eq. (11.7) gives WRP = 4389 lb. Thus the axial thrust is inward, and the separating force is away from the gear.
11.7.4 Bearing Loads The bearings selected must be adequate to support the axial forces Wx for both directions of rotation and for the load conditions on both sides of the teeth. Radial forces are transmitted indirectly through moment arms to the bearings. The radial bearing loads are derived from the gear separating force, the gear tangential force, and the gear thrust couple, along with the type of mounting and the bearing position.
11.7.5 Types of Mountings Two types of mountings are generally used: overhung, where both bearings are located on the shaft behind the gear, and straddle, where one bearing is on either side of the gear. Because of the stiffer configuration, straddle mountings are generally used for highly loaded gears.
11.7.6 Lubrication The lubrication system for a bevel- or hypoid-gear drive should sufficiently lubricate and adequately cool the gears and bearings. Splash lubrication is generally satisfactory for applications up to peripheral speeds of 2000 ft/min. The oil level should cover the full face of the lowest gear, and the quantity of oil should be sufficient to maintain the oil temperature within recommended limits.
Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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