Budynas-Nisbett:Shigley's Ill.Design of Mechanical 13.Gears-General T©The McGraw-Hil Mechanical Engineering Elements Companies,2008 Design,Eighth Edition Gears-General I 665 Thus,for a short period of time,there will be two teeth in contact,one in the vicinity of A and another near B.As the meshing proceeds,the pair near B must cease contact, leaving only a single pair of contacting teeth,until the procedure repeats itself. Because of the nature of this tooth action,either one or two pairs of teeth in con- tact,it is convenient to define the term contact ratio me as me = (13-8) D a number that indicates the average number of pairs of teeth in contact.Note that this ratio is also equal to the length of the path of contact divided by the base pitch.Gears should not generally be designed having contact ratios less than about 1.20,because inaccuracies in mounting might reduce the contact ratio even more,increasing the pos- sibility of impact between the teeth as well as an increase in the noise level. An easier way to obtain the contact ratio is to measure the line of action ab instead of the arc distance AB.Since ab in Fig.13-15 is tangent to the base circle when extended,the base pitch p must be used to calculate me instead of the circular pitch as in Eq.(13-8).If the length of the line of action is Lab,the contact ratio is Lab mc= (13-91 pcos中 in which Eq.(13-7)was used for the base pitch. 13-7 Interference The contact of portions of tooth profiles that are not conjugate is called interference. Consider Fig.13-16.Illustrated are two 16-tooth gears that have been cut to the now obsolete 14 pressure angle.The driver,gear 2,turns clockwise.The initial and final points of contact are designated A and B,respectively,and are located on the pressure line.Now notice that the points of tangency of the pressure line with the base circles C and D are located inside of points A and B.Interference is present. The interference is explained as follows.Contact begins when the tip of the driven tooth contacts the flank of the driving tooth.In this case the flank of the driving tooth first makes contact with the driven tooth at point A,and this occurs before the involute portion of the driving tooth comes within range.In other words,contact is occurring below the base circle of gear 2 on the nonimolute portion of the flank.The actual effect is that the involute tip or face of the driven gear tends to dig out the noninvolute flank of the driver. In this example the same effect occurs again as the teeth leave contact.Contact should end at point D or before.Since it does not end until point B.the effect is for the tip of the driving tooth to dig out.or interfere with,the flank of the driven tooth. When gear teeth are produced by a generation process,interference is automati- cally eliminated because the cutting tool removes the interfering portion of the flank. This effect is called undercutting:if undercutting is at all pronounced,the undercut tooth is considerably weakened.Thus the effect of eliminating interference by a gener- ation process is merely to substitute another problem for the original one. The smallest number of teeth on a spur pinion and gear,one-to-one gear ratio,which can exist without interference is Np.This number of teeth for spur gears is Robert Lipp."Avoiding Tooth Interference in Gears."Machine Design,Vol.54.No.1.1982.pp.122-124.Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 13. Gears — General 664 © The McGraw−Hill Companies, 2008 Gears—General 665 Thus, for a short period of time, there will be two teeth in contact, one in the vicinity of A and another near B. As the meshing proceeds, the pair near B must cease contact, leaving only a single pair of contacting teeth, until the procedure repeats itself. Because of the nature of this tooth action, either one or two pairs of teeth in con￾tact, it is convenient to define the term contact ratio mc as mc = qt p (13–8) a number that indicates the average number of pairs of teeth in contact. Note that this ratio is also equal to the length of the path of contact divided by the base pitch. Gears should not generally be designed having contact ratios less than about 1.20, because inaccuracies in mounting might reduce the contact ratio even more, increasing the pos￾sibility of impact between the teeth as well as an increase in the noise level. An easier way to obtain the contact ratio is to measure the line of action ab instead of the arc distance AB. Since ab in Fig. 13–15 is tangent to the base circle when extended, the base pitch pb must be used to calculate mc instead of the circular pitch as in Eq. (13–8). If the length of the line of action is Lab, the contact ratio is mc = Lab p cos φ (13–9) in which Eq. (13–7) was used for the base pitch. 13–7 Interference The contact of portions of tooth profiles that are not conjugate is called interference. Consider Fig. 13–16. Illustrated are two 16-tooth gears that have been cut to the now obsolete 141 2 ◦ pressure angle. The driver, gear 2, turns clockwise. The initial and final points of contact are designated A and B, respectively, and are located on the pressure line. Now notice that the points of tangency of the pressure line with the base circles C and D are located inside of points A and B. Interference is present. The interference is explained as follows. Contact begins when the tip of the driven tooth contacts the flank of the driving tooth. In this case the flank of the driving tooth first makes contact with the driven tooth at point A, and this occurs before the involute portion of the driving tooth comes within range. In other words, contact is occurring below the base circle of gear 2 on the noninvolute portion of the flank. The actual effect is that the involute tip or face of the driven gear tends to dig out the noninvolute flank of the driver. In this example the same effect occurs again as the teeth leave contact. Contact should end at point D or before. Since it does not end until point B, the effect is for the tip of the driving tooth to dig out, or interfere with, the flank of the driven tooth. When gear teeth are produced by a generation process, interference is automati￾cally eliminated because the cutting tool removes the interfering portion of the flank. This effect is called undercutting; if undercutting is at all pronounced, the undercut tooth is considerably weakened. Thus the effect of eliminating interference by a gener￾ation process is merely to substitute another problem for the original one. The smallest number of teeth on a spur pinion and gear,1 one-to-one gear ratio, which can exist without interference is NP . This number of teeth for spur gears is 1 Robert Lipp, “Avoiding Tooth Interference in Gears,” Machine Design, Vol. 54, No. 1, 1982, pp. 122–124