(1) Optimal modification of linear addendum with long tooth profile
Figures 1, 2 and 3 respectively show the simultaneous long tooth profile linear addendum modification of wheel and pinion gears, the long tooth profile linear addendum modification of only gear 1 (pinion gear), and the long tooth profile linear addendum modification of only gear 2 (wheel gear). In all figures, the ordinate represents Hertz contact stress, in N/mm2; The abscissa represents the transmission error, and the unit is μ m。 Scheme No. 0 on the drawing represents no modification, with Hertz contact stress of 553.412N/mm2 and transmission error of 0.319 μ m。 It can be seen from Fig. 3.29 that when the wheel and pinion gears are modified at the same time, the linear tooth top modification scheme with equal length tooth profiles of No. 1, No. 24 and No. 2 has a good effect. Compared with the unmodified scheme, the transmission error and Hertz contact stress have decreased, and the No. 1 scheme has the best effect. However, it can be seen from Figures 2 and 3 that if only the single gear in the helical gear pair is modified with long tooth profile linear addendum, the modification effect of all schemes is poor. Therefore, the preliminary optimization modification scheme of linear addendum with long tooth profile is No. 1 in the simultaneous modification of large and pinion gears, and the modification amount is 3 for large gears μ m. Pinion 3 μ m. Hertz contact stress and transmission error are reduced to 517.134N/mm2 and 0.263 respectively μ m。
(2) Optimal modification of circular arc addendum of long tooth profile
The large and pinion gears have long tooth profile arc tooth top modification at the same time, the pinion gears have long tooth profile arc tooth top modification only, and the wheel gears have long tooth profile arc tooth top modification only, as shown in Figures 4, 5 and 6 respectively. It can be seen from Fig. 4 that the modification schemes of the circular arc tooth top with long tooth profile for large and pinion gears such as No. 1, No. 2, and No. 48 at the same time have a good effect. Compared with the No. 0 scheme, the transmission error and Hertz contact stress of these modification schemes have been significantly reduced. The Hertz contact stress of No. 1 modification scheme is the lowest, 489.713N/mm2; The transmission error of Scheme 49 is the lowest, 0.266 μ m； The comprehensive performance of Scheme 48 is the best, with the Hertz contact stress of 525.853N/mm2 and transmission error of 0.274 μ m。 As this topic is not only to achieve vibration and noise reduction of helical gear pair, but also to improve the strength of gear teeth as much as possible, it is necessary to give consideration to both values, and select the 48 # scheme after comprehensive consideration, with the modification amount of wheel gear 5 μ m. Pinion 4 μ m。 Look again at Figures 5 and 6. Although the modification effects of each scheme in the two figures are not ideal, according to the previous analysis, the tooth profile modification is mainly to reduce Hertz contact stress and improve the strength and load capacity of helical gears; Tooth modification is mainly to reduce transmission error and affect the vibration noise of helical gears. Therefore, it is necessary to consider the possibility of reducing the Hertz contact stress by tooth profile modification, and then reducing the transmission error by tooth drum modification. However, No. 1, No. 2 and No. 3 in Figure 6 only reduce the Hertz contact stress of the long tooth profile arc tooth tip modification scheme of the wheel gear. After weighing, No. 1 scheme is also taken as the preliminary optimization modification scheme, and its modification amount is wheel gear 3 μ m. Pinion 0 μ m. Hertz contact stress and transmission error are 519.942N/mm2 and 0.327 respectively μ m。
(3) Optimal modification of involute addendum of long tooth profile
Figures 7, 8 and 9 respectively show the involute addendum modification of both large and pinion gears with long tooth profile, the involute addendum modification of only pinion gears with long tooth profile, and the involute addendum modification of only large gears with long tooth profile. It can be seen from Fig. 3.35 that there are many optimization schemes for the involute addendum modification of large and pinion gears with long tooth profiles at the same time. After weighing the transmission error and Hertz contact stress values, the No. 48 scheme is selected, and the Hertz contact stress and transmission error are 518.615N/mm2 and 0.300 respectively μ m. The modification amount is wheel gear 5 μ m. Pinion 4 μ m。 It can be seen from Figure 8 that if only the pinion is modified, the Hertz contact stress and transmission error values of all schemes will increase instead, so they are all rounded off. After observing Fig. 9, it can be seen that the Hertz contact stress of helical gear pair can be reduced by No. 1, No. 2 and No. 3 schemes, and the No. 1 scheme is the lowest, 513.825N/mm2. Therefore, the No. 1 scheme in the involute addendum modification mode of the long tooth profile of the wheel gear is also taken as the preliminary optimization modification scheme, and its modification amount is wheel gear 3 μ m. The pinion is not modified.
(4) Optimum modification of long tooth profile broken line circular arc addendum
Figures 10, 11 and 12 respectively show the modification of the broken line circular arc tooth top of the large and pinion gears with long tooth profiles at the same time, the modification of the broken line circular arc tooth top of the pinion gears with long tooth profiles only, and the modification of the broken line circular arc tooth top of the large gears with long tooth profiles only. It can be seen from Figure 10 that the modification effect of Scheme 1 and Scheme 24 is ideal, among which, Scheme 1 is the best, and its Hertz contact stress and transmission error are 532.917N/mm2 and 0.265 respectively μ m. The modification amount is wheel gear 3 μ m. Pinion 3 μ m。 It can be seen from Figure 11 that the values of transmission error and Hertz contact stress of schemes 10 to 23 are equal to those of the unmodified ones, and the modification effect of other schemes is worse, so all of them are excluded. After observing Figure 12, although there is no optimization scheme to reduce the transmission error and Hertz contact stress, Scheme 1, Scheme 2 and Scheme 3 all reduce the Hertz contact stress. Among them, No. 1 has a better effect, the Hertz contact stress is reduced to 529.8N/mm2, and the modification amount is wheel gear 3 μ m. The pinion is not modified.
(5) Optimized modification of tooth profile drum
Figures 13, 14 and 15 respectively show the simultaneous drum modification of the tooth profile of wheel and pinion gears, the drum modification of the tooth profile of pinion gears only, and the drum modification of the tooth profile of wheel gears only. It can be seen from Figure 13 that No. 1 is the only optimization scheme with ideal effect, and its Hertz contact stress and transmission error are 546.239N/mm2 and 0.284 respectively μ m. The modification amount is wheel gear 3 μ m. Pinion 3 μ m。 It can be seen from Figure 14 that, unlike other tooth profile modification methods, which only have poor effect on pinion after modification, the effect of No. 1, No. 2 and No. 3 modification schemes is relatively ideal. Among them, Scheme 1 has the best effect, with the Hertz contact stress and transmission error of 477.279N/mm2 and 0.267 respectively μ m. The modification amount is wheel gear without modification, and pinion gear 3 μ m。 It can be seen from Figure 15 that even if only the wheel gear is drum shaped, the modification effect of Scheme 1, Scheme 2 and Scheme 3 is very ideal, among which Scheme 1 is the best, with the Hertz contact stress and transmission error of 465.386N/mm2 and 0.279 respectively μ m. The modification amount is pinion gear without modification, wheel gear 3 μ m。
To sum up, it can be summarized as follows: 1. After the large and pinion gears of the helical gear pair are modified at the same time by using the above arbitrary tooth profile modification method, the optimal modification scheme with ideal effect can be obtained. 2. Except for the drum modification of tooth profile, if only the pinion of the helical gear pair is modified, the modification effect of other long tooth profile addendum modification methods is generally poor. 3. In addition to the linear modification of the tooth top of the long tooth profile (which can only slightly reduce the Hertz contact stress, while the previous research found that the tooth drum modification will increase the Hertz contact stress, so this method is excluded), if only the large gear modification of the helical gear pair is considered, then all the modification methods have an optimization scheme that can significantly reduce the Hertz contact stress. This is consistent with the analysis mentioned above that the tooth profile modification is mainly to reduce the Hertz contact stress of the helical gear pair, that is, to improve the strength (life) of the helical gear. 4. If the tooth profile drum modification method is adopted, it is necessary to analyze and compare the modification effect of the optimization scheme of simultaneous modification of wheel and pinion gears, and only the wheel gears or pinion gears, because the meshing performance of the helical gear pair after the optimization and modification of the three has their advantages and disadvantages.