716 Budynas-Nisbett:Shigley's Ill.Design of Mechanical 14.Spur and Helical Gears ©The McGra-Hfl Mechanical Engineering Elements Companies,2008 Design,Eighth Edition 718 Mechanical Engineering Design Table 14-2 Number of Number of Values of the Lewis Form Teeth Y Teeth Y Factor Y(These Values 12 0.245 28 0.353 Are for a Normal 13 0.261 30 0.359 Pressure Angle of20°， 14 0.277 34 0.371 Full-Depth Teeth,and a 15 0.290 38 0.384 Diametral Pitch of Unity 16 0.296 43 0.397 in the Plane of Rotation) 17 0.303 50 0.409 18 0.309 60 0.422 19 0.314 75 0.435 20 0.322 100 0.447 21 0.328 150 0.460 22 0.331 300 0.472 24 0.337 400 0.480 26 0.346 Rack 0.485 The use of Eq.(14-3)also implies that the teeth do not share the load and that the greatest force is exerted at the tip of the tooth.But we have already learned that the con- tact ratio should be somewhat greater than unity,say about 1.5,to achieve a quality gearset.If,in fact,the gears are cut with sufficient accuracy,the tip-load condition is not the worst,because another pair of teeth will be in contact when this condition occurs.Examination of run-in teeth will show that the heaviest loads occur near the middle of the tooth.Therefore the maximum stress probably occurs while a single pair of teeth is carrying the full load,at a point where another pair of teeth is just on the verge of coming into contact. Dynamic Effects When a pair of gears is driven at moderate or high speed and noise is generated,it is certain that dynamic effects are present.One of the earliest efforts to account for an increase in the load due to velocity employed a number of gears of the same size,mate- rial,and strength.Several of these gears were tested to destruction by meshing and loading them at zero velocity.The remaining gears were tested to destruction at various pitch-line velocities.For example,if a pair of gears failed at 500 Ibf tangential load at zero velocity and at 250 Ibf at velocity Vi,then a velocity factor,designated K.of 2 was specified for the gears at velocity Vi.Then another,identical,pair of gears running at a pitch-line velocity Vi could be assumed to have a load equal to twice the tangen- tial or transmitted load. Note that the definition of dynamic factor K has been altered.AGMA standards ANSI/AGMA 2001-D04 and 2101-D04 contain this caution: Dynamic factor K has been redefined as the reciprocal of that used in previous AGMA standards.It is now greater than 1.0.In earlier AGMA standards it was less than 1.0. Care must be taken in referring to work done prior to this change in the standards.Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 14. Spur and Helical Gears 716 © The McGraw−Hill Companies, 2008 718 Mechanical Engineering Design Number of Number of Teeth Y Teeth Y 12 0.245 28 0.353 13 0.261 30 0.359 14 0.277 34 0.371 15 0.290 38 0.384 16 0.296 43 0.397 17 0.303 50 0.409 18 0.309 60 0.422 19 0.314 75 0.435 20 0.322 100 0.447 21 0.328 150 0.460 22 0.331 300 0.472 24 0.337 400 0.480 26 0.346 Rack 0.485 Table 14–2 Values of the Lewis Form Factor Y (These Values Are for a Normal Pressure Angle of 20°, Full-Depth Teeth, and a Diametral Pitch of Unity in the Plane of Rotation) The use of Eq. (14–3) also implies that the teeth do not share the load and that the greatest force is exerted at the tip of the tooth. But we have already learned that the con￾tact ratio should be somewhat greater than unity, say about 1.5, to achieve a quality gearset. If, in fact, the gears are cut with sufficient accuracy, the tip-load condition is not the worst, because another pair of teeth will be in contact when this condition occurs. Examination of run-in teeth will show that the heaviest loads occur near the middle of the tooth. Therefore the maximum stress probably occurs while a single pair of teeth is carrying the full load, at a point where another pair of teeth is just on the verge of coming into contact. Dynamic Effects When a pair of gears is driven at moderate or high speed and noise is generated, it is certain that dynamic effects are present. One of the earliest efforts to account for an increase in the load due to velocity employed a number of gears of the same size, mate￾rial, and strength. Several of these gears were tested to destruction by meshing and loading them at zero velocity. The remaining gears were tested to destruction at various pitch-line velocities. For example, if a pair of gears failed at 500 lbf tangential load at zero velocity and at 250 lbf at velocity V1, then a velocity factor, designated Kv , of 2 was specified for the gears at velocity V1. Then another, identical, pair of gears running at a pitch-line velocity V1 could be assumed to have a load equal to twice the tangen￾tial or transmitted load. Note that the definition of dynamic factor Kv has been altered. AGMA standards ANSI/AGMA 2001-D04 and 2101-D04 contain this caution: Dynamic factor Kv has been redefined as the reciprocal of that used in previous AGMA standards. It is now greater than 1.0. In earlier AGMA standards it was less than 1.0. Care must be taken in referring to work done prior to this change in the standards