ON THE CONTACT STRENGTH OF DIFFERENT SECTIONS OF THE TOOTH PROFILE UNDER WEAR

Yu. S. Semenov, S. I. Shubovich

(Presented by the scientific seminar of the Departments of Applied and Theoretical Mechanics)

It is known that the contact endurance of the working surfaces of tooth tips is greater than the contact endurance of the surfaces of tooth flanks \[1–4\]. For this reason, pitting, which initially arises near the pitch line, spreads over the surfaces of the flanks and is rarely observed on the surfaces of the tips. The higher contact endurance of tooth tips, which has been called the tip effect, can be used to increase the load-carrying capacity of a gear transmission in which one of the gears has a relatively low hardness. For this purpose it is sufficient to choose such a correction of the meshing as would ensure an increase of the tip surface on the gear of lower hardness. In \[2\] it is shown that the use of the tip effect in some transmissions can provide an increase in load-carrying capacity, determined from the condition of resistance to pitting, by a factor of 2.7. It should be noted, however, that in some transmissions, when the tooth profiles are worn, a decrease is observed in the contact endurance of the surfaces of the tooth tips in comparison with their flanks; therefore, in such cases the use of the tip effect may lead not to an increase but to a reduction in the load-carrying capacity of the transmission. This will be shown below on the basis of the results of observations of the condition of the tooth surfaces of a transmission under wear.

At the Department of Applied Mechanics of the Tomsk Polytechnic Institute, an experimental investigation was carried out of the wear of the gear wheels of reducers for mining electric drills. Since one of the objectives of this investigation was to determine whether the serviceability of reducers for mining electric drills is limited by the contact strength of the gear wheels, the experiments included cases in which the teeth of the wheels were subjected to pitting not only in the near-pitch zone but also on other sections of their working surfaces. The present article aims to show and, to some extent, explain the results of these experiments.

The conditions under which the tests were conducted have been published earlier \[5\], and therefore we shall dwell on them here only briefly. The tests were carried out on a closed test rig. The object of the tests was a spur two-stage reducer of a mining electric drill ER-5. The gear wheels were made with teeth of a normal involute profile without finishing operations; the pinions were made of 20Kh steel with subsequent carburizing and hardening, and the wheels of 40Kh steel with subsequent hardening. The cleanliness of the tooth surfaces before testing corresponded to grade 6 according to GOST 2789-59.

The main part of the tests was carried out for two groups of hardness ratios of the pinion and the gear: 1. An optimal hardness ratio, at which the wear per tooth of the pinion and gear is close, and the total amount of wear is comparatively small. This group had: pinion hardness HRC = 55–60; gear hardness HRC = 40–45; numbers of teeth \(z_1 = 14\), \(z_2 = 46\); mesh module \(m = 1.5\) mm; circumferential speed \(v = 3.03\) m/sec. 2. A large difference in hardness, at which the wear of a gear tooth was tens of times greater than the wear of a pinion tooth. This group had: pinion hardness HRC = 55–60; gear hardness HRC = 30–35; \(z_1 = 17\), \(z_2 = 28\), \(m = 2\) mm, \(v = 1.49\) m/sec.

The tests were conducted both under constant loads of different magnitudes and under sharply varying loads. In both cases, in these experiments, judging from the wear curves, there were two periods of wear: the running-in period and the period of uniform (monotonic) wear [5], despite the fact that in the second period wear was accompanied by pitting of the working surfaces. Pitting initially arose in the pitch-line zone and then, depending on the transmission load, was either confined to the surface of the pitch-line zone or spread to the tooth tips of the driving gears of an accelerating transmission (Figs. 1, a and 2, a) and to the tooth roots of the driven gears of a reducing transmission (Figs. 1, b and 2, b). The tooth surfaces of pinions in transmissions with a large difference in hardness generally did not pit, while in transmissions with an optimal hardness ratio pitting occurred only in the pitch-line zone. Thus, the experimental results [5] show that not always and not under all operating conditions of a gear transmission do the tooth tips have greater resistance to pitting than the roots. In the works known to us it is not noted that the contact endurance of tooth tips depends on whether the gear is driving or driven.

Pitting of the tooth tips of driving gears and of the tooth roots of driven gears can be explained, in our opinion, by the different intensity of wear of the working surfaces of the driving and driven gears and by the laws governing the change in the geometry of tooth profiles during wear.

Professor A. I. Petrusevich notes in work [3] that deterioration of the conditions for formation of an oil film in the zone of tooth contact causes a certain wear of the surface which, in the absence of seizure, impedes pitting. At the moment when the root of a tooth of the driving gear meshes with the tip of a tooth of the driven gear, the conditions for the formation of an oil film are worse than at the moment when the tip of a tooth of the driving gear meshes with the root of a tooth of the driven gear [8]; consequently, the tooth tips of the driving gear should have less resistance to pitting than the tooth tips of the driven gear. This explanation would be sufficient if the maximum amount of wear occurred on the teeth of the driving gear at the root, and on the teeth of the driven gear at the tip. Our experiments show that, in both the driving and the driven gears, the tooth roots wear more than the tips. Consequently, the greater resistance to pitting of some surface cannot be explained solely by the wear of that surface. In our opinion, the contact endurance of one or another tooth surface also depends on the intensity of wear of the conjugate tooth surface of the mating gear.

In works [6, 7] it is shown that the laws governing changes in the geometric shape of tooth profiles during wear are such that the tooth-root surfaces undergo the greatest wear, and concavity arises in this region. Since the profile curves of interacting teeth are conjugate curves, on the tooth tips that come into contact with the concave profile of the tooth roots of the mating gear,

Fig. 1. Wheels of the first group: a) driving, b) driven. Constant load, contact stress*) $\sigma_k = 80\ \text{kg}/\text{mm}^2$.

Fig. 2. Wheels of the second group: a) driving, b) driven. Constant load, $\sigma_k = 104\ \text{kg}/\text{mm}^2$.

Fig. 3. Wheel of the first group, driving.
Sharply variable load from $\sigma_k = 48\ \text{kg}/\text{mm}^2$
to $\sigma_k = 80\ \text{kg}/\text{mm}^2$.

Fig. 4. Wheel of the second group, driving.
Sharply variable load from $\sigma_k = 61\ \text{kg}/\text{mm}^2$
to $\sigma_k = 104\ \text{kg}/\text{mm}^2$.

convexities are formed. Since the determining surface is the concave profile of the tooth dedendum, and the conditions for the formation of an oil film at the beginning of meshing are worse than at the end of meshing of a pair of teeth [8], the hollow on the dedendum of a tooth of the driving wheel is always larger than that of the driven one and, conversely, the convexity on the addendum of a tooth of the driving wheel is always smaller than that of the driven wheel.

Taking into account that progressive pitting occurs first of all where the possibility of wear is smaller, and also that the latter is determined by the degree of wear of the tooth dedenda, we conclude that the possibility of penetration of the addendum of a tooth of the driving gear into the dedendum of a tooth of the driven gear is less than that of the addendum of a tooth of the driven gear into the dedendum of a tooth of the driving gear. Therefore, in our experiments, on the driving wheel, following pitting of the near-pitch zone, the tooth addenda were pitted, while on the driven wheel—the tooth dedenda. The degree of pitting is determined by the ratio of the wear magnitudes of the teeth of the gear pair. As noted above, with an optimal hardness ratio the wear per tooth in the pinion and wheel is close in magnitude. Since in this case the degree of wear of the tooth dedendum of the driven pinion, which accelerates the transmission, is comparable with the degree of wear of the tooth dedendum of the driven wheel in a reducing transmission, the observed degree of pitting of the tooth addendum of the driving wheel here is close to the degree of pitting of the tooth dedendum of the driven wheel (Fig. 1).

With a large difference in the hardness of the mating teeth, the difference in the amounts of wear of the pinions and wheels is very large; therefore, even after running-in, the tooth dedendum of the driven wheel wears more intensively than the tooth dedendum of the driven pinion. This also explains why, with very strong pitting of the tooth addendum of the driving wheel, pitting of the tooth dedendum of the driven wheel is barely noticeable (Fig. 2). It should be noted that damage by pitting of the near-pitch zone of the driven wheel in this case is also weakly expressed. The latter, apparently, is explained by the drawing of material into the near-pitch zone of the driven wheels, analogous to what was noted by G. K. Trubin [4].

The phenomena described are observed both under constant and under sharply variable loading. Figs. 3 and 4 show the teeth of the driving wheels of the first and second groups, which operated under sharply variable loading.

As can be seen from Figs. 3 and 4, under sharply variable loading, pitting both in the near-pitch zone and on the tooth addenda is expressed even more distinctly than under constant loading. The portions of the surface of the tooth dedenda remote from the pitch point, however, did not pit, as also occurred under constant loading for the driving wheels.

Thus, it may be concluded that, since tooth addenda do not under all operating conditions of a transmission possess greater resistance to pitting than dedenda, the use of the addendum effect in the presence of tooth wear in a reducing transmission will increase, while in an accelerating transmission, on the contrary, decrease its load-carrying capacity.

REFERENCES

1. V. N. Kudryavtsev. Gear Transmissions. Mashgiz, Moscow–Leningrad, 1957.

2. I. M. Kilimov. Calculation of gear transmissions with a difference in hardness of the working surfaces of the teeth. Collection of Works of LMI, No. 15, Leningrad, 1960.

3. A. I. Petrusevich. The role of the hydrodynamic oil film in the resistance and durability of contact surfaces of machine parts. Vestnik mashinostroeniya, No. 1, 1963.

4. G. K. Trubin. Contact Fatigue of the Teeth of Spur Gears. Mashgiz, Moscow, 1950.

5. Yu. S. Semenov. Investigation of the wear of gear wheels of mining electric-drill reducers. Proceedings of the Conference on Problems of Calculation, Design, and Research...

gear transmissions and flexible-link transmissions, 1957, vol. III, publ. Odessa Polytechnic Institute, 1959.

1. Yu. S. Semenov. Some regularities in the wear of gear wheels. Izvestiya TPI, vol. 96, pt. 2, publ. Tomsk University, Tomsk, 1961.

2. Yu. S. Semenov. Changes in the parameters of gear meshing under wear. Izvestiya TPI, vol. 96, pt. 2, publ. Tomsk University, Tomsk, 1961.

3. Ya. G. Kistyan. Experimental study of the process of seizure of the surfaces of the teeth of spur gears. Proceedings of the Conference on Problems of the Calculation, Design, and Study of Gear Transmissions and Flexible-Link Transmissions, 1957, vol. III, publ. Odessa Polytechnic Institute, 1959.