SOME REGULARITIES OF GEAR WHEEL WEAR

Yu. S. SEMENOV

(Presented by the scientific seminar of the Department of Applied Mechanics)

The characteristic of wear of the working surfaces of the teeth of gear wheels is usually taken to be the specific work of friction, or the proportional specific sliding \[1\]. If one follows this proposition, then it is impossible to explain, for example, the wear of teeth in the near-pitch zone of the working surface, since in this zone the quantities indicated above are very small. In this connection some authors, for example \[2\], try to introduce a new parameter characterizing wear which is devoid of physical meaning but provides better agreement of theoretical calculations with experimental data on wear in the near-pitch zone.

In the present article, using as an example the analysis of the profiles of worn teeth of a real transmission that was subjected to tests \[3\], it will be shown that the specific work of friction can be a characteristic determining the change in the geometry of the profiles of involute teeth under wear, provided that the change of this characteristic is taken into account in connection with the change in the geometry of meshing during the wear process \[4\].

Fig. 1. Change of tooth profiles in the process of wear. Under load and corresponding contact stress $\sigma_k = 10500\ \mathrm{kg/cm^2}$: a) tooth of the driving wheel; b) tooth of the driven wheel.

Our observations of the condition of the working surfaces and the geometry of the tooth profiles during wear tests made it possible

establish three characteristic zones¹ on the working surfaces (Fig. 1), differing in the type of surface and in the outline of the profile. The first zone (in the region of the tooth tip) always has a convex profile and a smooth, shiny surface with small scratches in the direction of sliding; the second zone (in the region of the pitch circle) may have either a convex or a concave profile, and its surface is matte; the third zone (on the tooth root) always has a concave profile and a surface similar to that of the first zone. The boundaries of these three

Fig. 2. Meshing of experimental gear wheels that quickly ran in under wear. Contact stress \(\sigma_k = 8700\ \mathrm{kg/cm^2}\). The zone of single-pair meshing of the wheel tooth before wear is \(cd\), after wear \(mn\).

zones are clearly expressed and coincide with the points on the profile corresponding to the beginning and end of single-pair meshing (Fig. 2).

It is expedient to consider the regularities in the change of the geometrical form of the tooth profiles for the first and third zones together, and for the second separately.

Wear of the first and third zones

In the first period of operation of involute gearing, on the roots of the teeth of both wheels of the gear pair the magnitude of the specific work of friction has a sharply expressed maximum [1]; therefore the surfaces of the tooth roots are subjected to the greatest wear, and concavity arises on this portion of the profile. Since the kinematics of gear meshing is such that the profile curves of a pair of interacting teeth are conjugate, convexities necessarily form on the tips of the teeth that come into contact with the concave profile of the tooth roots. Consequently, in the formation of tooth profiles in the regions of the first and third zones, the profile of the tooth root is the determining one.

If it is taken into account that the specific work of friction on the root of the pinion tooth is considerably greater than on the root of the wheel tooth, then it may be concluded that the hollow on the root of the pinion tooth and the convexity on the tip of the wheel tooth will be more clearly expressed than the concavity of the hollow of the wheel-tooth root and the convexity of the pinion-tooth tip. What has been said is confirmed by our experiments (Figs. 2 and 3).

As the geometry of the tooth profiles changes, the distribution of the values of specific sliding and of the specific work of friction along the tooth profile becomes more even; their maxima decrease and gradually shift toward the pitch pole \[4\]. Therefore the place of maximum wear shifts in the same direction; consequently, the boundaries of the hollow on the tooth dedendum and, correspondingly, of the convexity on the addendum of the mating tooth expand more and more toward the near-pitch zone (Fig. 1).

However, as a consequence of the smoothing of irregularities on the working surfaces of the teeth, and also of the above-mentioned redistribution of the values of specific sliding and of the specific work of friction, the rate of wear becomes slower and slower, until at last it assumes the character of uniform (monotonic) wear. In this period the regularities indicated above also take place, but, owing to the slowing of the rate of integral (total) wear, they manifest themselves much more weakly: the hollow of the tooth dedendum and the convexity of the tooth addendum, although they expand toward the near-pitch zone, do so with a considerably reduced intensity. What has been said is illustrated by the geometry of the profiles shown in Figs. 1a, 1b, for different stages of wear corresponding in time to the points plotted on curves 4 and 3 of Fig. 4.

Fig. 3. Meshing of experimental gear wheels that had been slowly run in under wear. Contact stress \(\sigma_k = 8700\ \mathrm{kg/cm^2}\).

Fig. 4. Wear graph of the teeth of the wheels shown in Figs. 1, 2, 3. Solid lines—the driving wheels; dashed line—the driven wheel. Circles mark the beginning of progressive bulging of the near-pitch zone.

Wear of the Second Zone

Following the change in the geometric form of the tooth profiles in the first and third zones, the values of specific sliding and of the specific work of friction in the second zone increase, and their maxima shift more and more toward the pitch pole. Hence the wear of the tooth regions of the second zone gradually intensifies; the character of the change in profile geometry depends to a large extent on the ratio of the hardnesses of the mating surfaces, the running-in time, and the magnitude of wear during this period. The profile of the less hard surface (in our case, the tooth profile of the wheel) in this zone may be described both by a convex (Figs. 1 and 2) and by a concave (Fig. 3) curve, while the mating profile of the pinion tooth (the harder surface) will in both cases be a convex curve.

If the running-in period is comparatively short (curves 4, 3, 1 in Fig. 4 and, respectively, Figs. 1 and 2), and if the gear wears comparatively little during this period, while the profile of its teeth in the near-pitch zone differs little from an involute, then the magnitudes of the specific sliding and the specific work of friction, although greater than the initial ones, will still have their maxima not shifted into the near-pitch zone and, consequently, the hollow at the tooth root will not yet extend to the near-pitch portion of the tooth. In this case the tooth profile of the wheel in the second zone will be traced by a convex curve (Figs. 1 and 2).

During the period of monotonic (steady) wear, although there is a tendency for the maxima of the specific sliding and the specific work of friction to shift toward the mesh pole, owing to the low intensity of the overall wear in this period the maxima of the indicated quantities shift slowly; therefore the profiles of the second zone remain convex.

The occurrence, during the period of uniform wear, of progressive pitting of the near-pitch zone, while contributing to wear and somewhat reducing the convexity of the profile of this zone, nevertheless does not introduce fundamental changes into the character of the tooth-profile curve.

If the running-in period is comparatively long (curve 2 in Fig. 4 and, respectively, Fig. 3), then already in this period the maxima of the specific sliding and the specific work of friction gradually move directly into the near-pitch zone; the hollow at the tooth root will also extend into this region, and the tooth profile of the wheel in the second zone will be traced by a concave curve. The subsequent period of uniform wear, as well as the pitting of the near-pitch zone that occurs during this period, also do not noticeably change the character of the curves of the tooth profiles. Therefore it should be noted that the progressive pitting of the near-pitch zone observed in our experiments does not have a substantial effect on the wear of the teeth of the gears under investigation. However, with wear, owing to the widening of the zone of single-pair engagement and the increase of friction forces on portions of the tooth profiles remote from the pole, the contact strength of the surface of these portions decreases [4]. Thus, in our experiments [3], under a sufficiently large load, a whole series of cases of pitting of the tooth tips of the driving gears and of the tooth roots of the driven wheels was observed. In this case the tooth tips of the driving gears wear down to a sharp edge (Fig. 1a), bend, and break off. In the process of wear, the tooth section that is dangerous with respect to bending stresses gradually moves in the direction from the tooth root toward the tooth tip.

Thus, when assessing the serviceability of a gear transmission, it is important to know not only the integral magnitude of tooth wear in the form of a curve reflecting the wear process over time, but also its relation to the change in the geometric shape of the tooth profiles, since only in this case can one judge more fully the factors that, in the particular case in question, exert the predominant influence on wear of the tooth profile. At the same time, from the shape of the worn profile one can judge the character of the curve of integral wear as a function of time and, conversely, from the form of the wear curve one can draw a conclusion about the character of the geometric shape of the worn profile. When comparing various parameters that determine the character of wear of tooth profiles, it is necessary to take into account the dynamics of wear of gear engagement, since the parameters themselves do not remain constant but, on the contrary, change continuously together with the change in the shape of the tooth profiles under wear. The specific—

… sliding and the specific work of friction, as follows from the analysis carried out, may be parameters determining the character of the change in the geometric form of the profiles of worn teeth.

References

1. Kh. F. Ketov, N. I. Kolchin. Theory of Mechanisms and Machines. Mashgiz, 1939.

2. A. D. Nevskii. On the question of tooth wear. Scientific Reports of Higher Education: Machine Building and Instrument Engineering, No. 2, 1959.

3. Yu. S. Semenov. Results of an experimental study of the wear of gear wheels of gearboxes of mining electric drills. Proceedings of TPI, vol. 108, Study of Drilling Machines, Metallurgizdat, Sverdlovsk, 1959.

4. Yu. S. Semenov. Change in the parameters of gear meshing under wear (published in the present collection).

5. B. I. Kostetskii. Wear Resistance of Machine Parts. Mashgiz, Kiev—Moscow, 1950.

1. Similar zones have been observed by other authors, in particular by B. I. Kostetskii [5]. ↩