Wear and Cleanliness of the Working Surfaces of Gear-Wheel Teeth

Yu. S. Semenov, V. T. Gorbenko

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

As one of the measures for increasing the load-carrying capacity of gear transmissions, the use of a large difference (drop) in the hardnesses of the working surfaces of the teeth of the pinion and the wheel is recommended [1]. However, in this case, if the working surface of the pinion teeth is insufficiently clean, as is known, considerable wear of the wheel teeth is possible.

At the Department of Applied Mechanics of Tomsk Polytechnic Institute, work was carried out to investigate the wear of the gear wheels of mining electric-drill gearboxes [2], [3], including under a large difference in the hardnesses of the teeth of the pinion and the wheel. The gearboxes of mining electric drills belong to a broad group of gear transmissions used in general machine building; after heat treatment, the working surfaces of the teeth of the gear wheels in this group are usually not subjected to finishing operations [4]. The question arises whether it is necessary to apply finishing operations after heat treatment in order to avoid heavy wear in the case of a significant difference in the hardnesses of the gear pair, or whether some increase in the cleanliness of the working surfaces during tooth cutting before heat treatment is sufficient. In addition, it was of interest to determine the nature of the change in the cleanliness of the working surfaces of the teeth and in the coefficient of friction during wear, as well as the nature of the destruction of the working surfaces of the teeth and the change in the geometric form of the profiles of worn teeth at different initial cleanlinesses of their working surfaces. For this purpose, in addition to the tests [2], [3], at the maximum of the loads used, experiments were performed by engineer V. T. Gorbenko, the conditions of which for the low-speed stages of the gearboxes under test differed from [2], [3] by a higher initial cleanliness of the working surfaces of the teeth, with values of the tooth hardnesses of the pinion and wheel close to those in [2], [3]. The initial cleanliness of the working surfaces of the teeth of the gear wheels used in these experiments was ensured, as in [2], [3], in the process of cutting the teeth before heat treatment. No finishing operations after heat treatment were used in either case. The characteristics of the experimental gear wheels and of the test regimes are given in Tables 1 and 2.

The tests were carried out on a closed-loop installation. For lubricating the gear wheels and the bearings, con-

Table 1

Characteristics of the experimental gear wheels

Note: In parentheses are indicated the hardness and finishing of the gear teeth of group 5. The group designation is given in Table 2.

Consistent grease lubrication (solidol M) was used, filling approximately \(2/3\) of the housing volume. The cleanliness of the working surfaces of the teeth of the gear wheels was determined with a Linnick double microscope from impressions made of gutta-percha compound [5]. The impression method was first checked. For this purpose a pinion tooth was cut out, and the data from measurements of the surface cleanliness directly on the tooth and on its impression were compared. The results of the measurements, taking into account the coefficient allowing for rounding of the peaks on the impression \(K=1.05\) [5], were identical. In addition, after completion of the wear test a tooth was cut out of the wheel and the cleanliness of its surface was determined on a profilograph-profilometer. The magnitude of the integral wear of the teeth was determined by weighing the gear wheels on an analytical balance. The distribution of wear over the tooth profile and the nature of the change in the tooth profiles during wear were determined on a projector at a magnification of \(X50\). The change in the condition of the working surfaces of the teeth was established visually.

The tests showed that, during wear, the initial cleanliness of the working surfaces of the teeth changes. At the same time, the size and direction of the irregularities change. If before wear the maximum irregularities were located along the tooth, parallel to the axis of the wheel, then after wear they are located across the tooth in the direction of sliding during friction. Before the test, the height of the irregularities in the direction of machining of the tooth (i.e., in the direction parallel to the axis of the wheel) was 3–3.5 times greater than in the perpendicular direction. After the tests, the height of the irregularities located along the tooth decreases tens of times in comparison with the initial value, and the nature of the irregularities changes. If before the test, on a new tooth, the distances between ridges were 0.1–0.3 mm, then after the test the irregularities acquire a smoother, more gently sloping character, and the distances between them are 0.5–0.8 mm.

The irregularities on the surface of the teeth in the direction of sliding (perpendicular to the axis of the wheel) after wear may both decrease,

Regimes of loading and cleanliness of the working tooth surfaces

Table 2

Notes:
1) A group denotes identical gear pairs in terms of initial cleanliness and load.
2) In the numerator is the average value of the moment at the end of the test for the driving gear wheels; in the denominator, the same value for the driven ones.

which, for example, occurred under small loads, and also increase in height in comparison with the initial magnitude of the irregularities in this direction. In this case, however, their height is always less than the initial height of the irregularities in the direction of machining. The character of the irregularities located in the direction of sliding also changes during wear. They take the form of a smooth wavy line, with distances between crests of approximately \(0.05\)—\(0.15\) mm.

The finish of the working surfaces at different sections along the tooth height after wear is not the same. As noted in [2], [3], during wear on the working surface of a tooth three characteristic zones, different in appearance, are distinguished: at the tooth tip, in the middle of the tooth at the pitch line (on both sides of it), and at the tooth root. After wear, as a rule, the first and third zones have a smoother surface, while the near-pitch zone has a rougher surface (Table 2).

The tests also showed that, in the wear of gear wheels, the propositions noted by Prof. P. E. Dyachenko [6] are fully confirmed: namely, that the finish of the surface after wear is determined by the conditions of wear (i.e., by the operating regime of the mesh). In our tests only the magnitude of the load was varied; otherwise (sliding speed, lubrication, etc.) the operating regime of the gear wheels was kept constant. It is seen from Table 2 that, with the same initial finish of the tooth surfaces and different loads (groups 1, 2, 3, and 4), the finish of the working surfaces after wear will be different; moreover, the lower the load, the higher the surface finish after wear. Conversely, with different initial finish and the same load (groups 4 and 5), after wear approximately the same finish of the working surfaces of the teeth is obtained.

Together with the change in finish of the working surfaces of the teeth, the coefficient of friction in the mesh changes. Figure 1 shows the change in the coefficient of friction in the mesh during tooth wear for various

Fig. 1. Change in the coefficient of friction in the mesh during tooth wear. The curve designations correspond to the group number of the pairs of gear wheels according to Table 2.

loads used in our tests. As can be seen from Fig. 1, in the initial period of operation of the gear pair (the running-in period), the coefficient of friction decreases. By the end of the running-in period, at each load, a definite value of the coefficient of friction is established, which thereafter practically does not change throughout the entire test period, despite considerable wear and spalling of the working surfaces of the teeth of the gear wheels. At the same time, the character of the change in the coefficient of friction corresponds to the character of the change in the finish of the working surfaces of the teeth. With the same initial finish and different loads, curves 1, 2, 3, and 4 (Fig. 1), the coefficient of friction at first

is approximately the same, and then, in the process of wear, its value changes differently: the lower the load, the smaller the value of the coefficient of friction after wear. With different initial cleanliness and the same load (curves 4 and 5, Fig. 1), the coefficient of friction in the mesh is different at first, and then, after wear, its value becomes almost the same. Thus, the cleanliness of the working surfaces of the teeth has a decisive influence on the value of the coefficient of friction in the mesh.

During wear, as was indicated, three characteristic zones are distinguished on the working surface of the tooth, differing in the appearance of the surface and in the outline of the profile. The boundaries of these three zones are clearly expressed and coincide with the boundaries of the zone of single-pair contact on the tooth profile. The change in the condition of the surfaces of these zones during wear for groups of gear-wheel pairs 1, 2, 3, and 4 (Table 2) is described in [2], [3]. During running-in, the first and third zones (on the tooth tip and root) have a smooth shiny surface with small scratches in the direction of sliding, whereas the second (near-pitch) zone has a matte surface. Under a comparatively small load (1st group of pairs, Table 2), the condition of the surfaces of all zones remained almost unchanged, without signs of characteristic progressive pitting throughout the entire test period. Under medium loads (groups of pairs 2 and 3, Table 2), the surfaces of the first and third zones had the same appearance as in the first group; on the surface of the second zone of the wheel, near the pitch line, pitting appeared with time, which then spread over the entire surface of the second zone (both below and above the pitch line) and did not cease during the whole test period. Under the greatest load used in the tests (group 4, Table 2), after the pitting had spread over the entire surface of the second zone, pitting appeared on the first zone (tooth tip) of the driving wheels (speed-increasing transmission) and on the third zone (tooth root) of the driven wheels (speed-reducing transmission). The teeth of the pinions were not subject to pitting under any loads.

In tests of gear wheels with a higher initial cleanliness of the tooth surfaces (group 5, Table 2), the nature of the change in the condition of the working surfaces was the same as for the gear wheels of group 4, which operated under a load of the same magnitude; the difference was only in the amount of wear. Fig. 2 presents photographs of the working surfaces of the teeth of the driving and driven wheels of both groups, from which it is seen that, despite the different magnitude of integral wear, the condition of the tooth surfaces of the wheels of both groups is the same. After the tests, on the teeth of the driving wheels of both groups the pitting pits are located on the surface of the second and first zones, and on the teeth of the driven wheels—of the second and third zones. The time of onset of progressive pitting also approximately coincides in both groups. In both cases pitting began after completion of running-in and the onset of a period of uniform (monotonic) wear.

Owing to the different friction conditions on different portions of the working surfaces of the teeth, the tooth profiles wear unevenly [2], [3]. After wear, the first zone (in the region of the tooth tip) always has a convex profile; the second zone (in the region of the pitch circle) on the wheel (the less hard surface) may have either a convex or a concave profile, while on the pinion (the harder surface) it has a convex profile; the third zone (on the tooth root) always has a concave profile. An explanation of the regularities in the change of the tooth profiles is given in [7]. The above also occurs during wear of gear wheels with a higher initial cleanliness of the working tooth surfaces. Fig. 3 shows the meshes of gear pairs of speed-reducing transmissions from groups 4 and 5 (Table 2).

after wear; moreover, from group 5 a gear pair was taken whose worn-tooth profiles differ most strongly from the original involute profiles. Before testing, the gear-pair groups 4 and 5 had different degrees of tooth-surface cleanliness and were tested under identical loads. From Fig. 3 it is seen that the change in the tooth profiles of both groups during wear is of a general character, although the magnitude of wear of their gear wheels is different. The change in the line of action is also of a general character. As is seen from Fig. 3, in both cases the lines of action are transformed from the straight line \(ab\) into the curve \(KK_1 P K_2K_3\), and hence the other parameters of meshing also change [8].

Fig. 2. Condition of the working surfaces of worn teeth: I—wheels of group 4; II—wheels of group 5; a) teeth of driving wheels; b) teeth of driven wheels.

A change in the meshing parameters affects the wear intensity and the contact strength of a gear transmission. As noted in [7], [8], during wear the friction losses in the mesh decrease, the values of the specific sliding and the specific friction work are evened out along the tooth profile, and their maxima decrease; this contributes to a reduction in the intensity of wear. On the other hand, the contact ratio decreases, the zone of single-pair meshing expands, and the normal pressure of the interacting teeth (and, consequently, the friction force) increases on portions of the tooth profiles remote from the pitch circle, which leads to a decrease in the contact strength of these portions. As is seen from Fig. 3, in the gear pair with the higher initial cleanliness of the tooth surfaces (group 5), even in the case of the greatest change in the geometrical form of the profiles of the worn teeth, owing to the smaller magnitude of the integral wear, the line of action on

over the segment \(P K_2 K_3\) is distorted less than in the gear pair of group 4. Hence, in the gear pair of group 5 the length of the arc of contact \(g_2 g_2'\) is greater and, consequently, the contact ratio is higher. Thus, for the gear engagements shown in Fig. 3, the contact ratio after wear

Fig. 3. Meshing of worn gear wheels: I — gear pair of group 4; II — gear pair of group 5.

is: for the gear pair of group 4, \(\varepsilon = 1.03\); for the gear pair of group 5, \(\varepsilon = 1.14\). Consequently, in the case of a higher initial cleanliness of the working surfaces of the teeth, the adverse effect of the phenomenon of a decrease in the contact ratio and an increase in the zone of single-pair meshing during wear will have a lesser influence on the operation of the transmission.

Figure 4 shows the graphs of the integral wear of the experimental gear wheels, from which it can be seen that, in our tests, there were basically two periods of wear: the running-in period, i.e., a period of gradual slowing of the wear rate as a result of changes in

Fig. 4. Wear graphs: a) pinions, b) wheels. The designations of the curves correspond to the group number of the pairs of gear wheels according to Table 2. Solid lines—driving pinions and wheels; dashed lines—driven pinions and wheels.

the wear conditions (an increase in the cleanliness of the tooth surfaces, running-in of the profiles, etc.) and a period of uniform (monotonic) wear, characterized by constancy of the wear conditions [9], although tooth spalling of the wheels (the surface with lower hardness) occurred in this case. Moreover, as noted above, with the greatest of the appli-

...of the loads occurring in our tests, the scuffing did not cover only the surface of the second zone, but occurred in the first zone of the teeth of the driving wheels and in the third zone of the teeth of the driven wheels. With the same initial cleanliness of the tooth surfaces, the rate of wear, characterized by the angle of inclination of the wear curves, increases with increasing load; moreover, the wear rate of the driving gears is usually higher than that of the corresponding driven gears. It is necessary, however, to note that, as is evident from Fig. 4a, the pinions at medium loads (groups 2 and 3) wore more strongly than at the highest load (group 4); this phenomenon occurred in tests [2], [3] only with a large difference in the hardnesses of the teeth of the pinion and the wheel. From the graphs in Fig. 4 it is also evident that, in the case of a lower initial cleanliness of the tooth surfaces (groups 1, 2, 3, and 4), the amount of wear of the wheel teeth is greater than the amount of wear of the pinion teeth. At high load the difference in the magnitudes of wear of the teeth of the wheels and pinions is very great. In the case of a higher initial cleanliness of the tooth surfaces (group 5), although the amount of wear of the wheel teeth is somewhat greater than the amount of wear of the pinion teeth, the difference between these quantities is small. The amount of wear of the pinion teeth of group 5 is approximately the same as that of the pinions of group 4, which worked under the same load. The wear of the wheel teeth of group 5, however, is much less than the wear of the corresponding wheels of group 4.

Thus, it may be concluded that, in the case of the use of gear transmissions with a large difference in hardness between the surfaces of the teeth of the pinion and the wheel, a certain increase in the cleanliness of the working surfaces in the process of cutting the teeth before heat treatment has little effect on the degree of cleanliness of the working tooth surfaces formed during wear, on the value of the coefficient of friction in the mesh after running-in of the teeth, on the condition of the surfaces after wear and the contact strength, and also on the geometrical form of the worn profile; but it substantially reduces the amount of total wear of the wheel teeth, chiefly during the running-in period. Consequently, in those cases where, in the manufacture of gears, the use of finishing operations after heat treatment is undesirable, it is advisable to obtain the highest possible cleanliness of the tooth surfaces before heat treatment.

LITERATURE

1. I. M. Kilimov. Calculation of gear transmissions with a difference in hardness of the working surfaces of the teeth. Collected Papers of LMI, No. 15, Leningrad, 1960.

2. 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 Investigation of Gear Transmissions and Flexible-Coupling Transmissions, 1957, vol. III, Publishing House of the Odessa Polytechnic Institute, 1959.

3. Yu. S. Semenov. Results of an experimental investigation of wear of gear wheels of mining electric-drill reducers. Izvestiya TPI, vol. 108. Investigation of Drilling Machines. Metallurgizdat, Sverdlovsk, 1959.

4. L. D. Chasovnikov. Transmissions by Meshing. Mashgiz, 1961.

5. K. I. Abadzhy, A. N. Boitsov, F. P. Volosevich, P. N. Goberman, A. K. Kutai, F. I. Naripskii, G. A. Oding, A. D. Rubinov, G. A. Shtyurmer. Handbook of Production Control in Machine Building. Mashgiz, Moscow—Leningrad, 1956.

6. P. E. Dyachenko. Influence of Technological Factors on Wear of Metals. Increasing the Wear Resistance and Service Life of Machines. Mashgiz, Kiev—Moscow, 1953.

7. Yu. S. Semenov. Some regularities of wear of gear wheels. Izvestiya TPI, vol. 96, part 2, Publishing House of Tomsk University, Tomsk, 1961.

8. Yu. S. Semenov. Change in the parameters of gear meshing during wear. Izvestiya TPI, vol. 96, part 2, Publishing House of Tomsk University, Tomsk, 1961.

9. A. S. Pronikov. Wear and Durability of Machine Tools. Mashgiz, Moscow, 1957.