NEWS
OF THE TOMSK ORDER OF THE RED BANNER OF LABOR POLYTECHNIC
INSTITUTE named after S. M. KIROV

Volume 147
1966

ON THE EFFICIENCY OF GEAR TRANSMISSIONS OF A TWO-STAGE REDUCER WITH CONSISTENT GREASE LUBRICATION

Yu. S. SEMENOV

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

As is known, in gear reducers lubrication with liquid oil is used mainly, being carried out predominantly by dipping the teeth of the wheels into the oil bath of the reducer. Consistent (thick) grease is usually used only for open gear transmissions. It is considered that the friction conditions with consistent grease lubrication are worse than with liquid-oil lubrication. In our opinion, such a conclusion is based only on the experience of using consistent grease in open transmissions. In the literature, for example [1], information is given on the efficiency of single-stage and two-stage enclosed transmissions (reducers) with liquid lubrication and of open single-stage transmissions with thick grease. However, in the literary sources known to us there is almost no information on the efficiency of enclosed transmissions when operating with consistent grease. Meanwhile, the use of consistent grease in gear reducers is in many cases very convenient and justified.

At the Department of Applied Mechanics of the Tomsk Polytechnic Institute an experimental study was carried out of the wear of the gear wheels of reducers of mining electric drills. Since, under the conditions of convenient operation, these reducers work with consistent grease, one of the tasks was to investigate the efficiency of enclosed gear transmissions when operating with consistent grease. The present article aims to show some results of this study.

The conditions under which the tests were carried out, as well as a description of the experimental installation and the formulas by which the efficiency of the gear transmissions was determined, have been published earlier [2], [3], [4], and therefore we do not present them here. We note only that the object of the tests was the spur two-stage reducer of the ER-5 mining electric drill [5]. For lubrication of the gear wheels and bearings, consistent grease (solidol M) was always placed into the reducer housings in the same quantity; it filled approximately 2/3 of the housing volume.

The magnitude of the efficiency of the reducer changes both during the working day and over the entire duration of the tests. This change in efficiency is connected with the change in grease temperature and with the change in the condition of the tooth surfaces during wear. Let us consider the influence of these factors separately. We shall dwell on the influence of grease temperature on the efficiency of the reducer. In order, as far as possible, to exclude the influence of tooth wear, we shall take the period of uniform wear [2, 3], when the amount of wear is relatively small.

The temperature of the lubricant in the reducer oil bath and its efficiency are directly related to one another. On the one hand, the increase in temperature is determined by the magnitude of the power lost to friction in the gearing and in the bearings, and also to churning of the lubricant. On the other hand, the lubricant temperature affects the magnitude of the power losses in the reducer, mainly the no-load losses. During operation of a gear reducer, the temperature of the lubricant in its oil bath rises until a steady thermal regime is established. Fig. 1 gives an example of a typical change in the lubricant temperature in the oil bath of the reducers tested over the course of the working day under various

Fig. 1. Change in lubricant temperature and reducer efficiency over the course of the working day.
Solid lines—graphs of the change in efficiency; dashed lines—graphs of the change in lubricant temperature. The numerals 1–8 denote the load magnitude, corresponding to 1 and 5 \(M = 270\ \text{kgcm}\); 2 and 6 \(M = 475\ \text{kgcm}\); 3 and 7 \(M = 525\ \text{kgcm}\); 4 and 8 \(M = 740\ \text{kgcm}\), where \(M\) is the torque on the housing of the loading reducer [4].

loads that occurred in our tests. Here it is appropriate to note that no appreciable difference is observed in the lubricant temperature in the oil bath of identical speed-increasing and speed-reducing transmissions, either in the character of its change during the working day or in its magnitude. As a rule, the temperature in the oil bath of a speed-reducing transmission is somewhat lower than that of a speed-increasing one; however, the difference is very small, on the order of \(1\)–\(2^\circ\text{C}\), which indicates close values of the efficiency of the speed-reducing and speed-increasing transmissions. This is evidently explained by the fact that, in general, the difference in the efficiency of the gear meshes of speed-increasing and speed-reducing transmissions is comparatively small and, moreover, the efficiency of the mesh constitutes only part of the overall efficiency of the reducer. The losses due to friction in the bearings, to churning and splashing of the lubricant, and to friction of the rotating parts against the air are practically the same in speed-reducing and speed-increasing transmissions. In other words, their no-load losses and the bearing losses due to load are practically the same.

As can be seen from Fig. 1, the lubricant temperature changes substantially during the first hour of reducer operation; then it changes more slowly, and usually after two hours of operation a steady thermal regime is established. At maximum load, in all tests approx-

but two hours after the start of operation of the reducer, a temperature maximum occurs, followed by a certain slight decrease in the subsequent hours of operation. In order to determine whether this is a consequence of severe wear of the teeth of the gear wheels in the initial stages of operation of reducers tested at maximum load, or of some other factors inherent only in these reducers, an experiment was carried out in which one and the same reducer was tested at different loads. For this purpose, reducers were used that had previously been tested at maximum load, after the wear of the teeth of their gear wheels had acquired a uniform (monotonic) character. These tests were carried out for a short time, for 8 hours at each load; each time, before switching to another load, the reducers were washed and fresh lubricant was placed in them, always in the same quantity. The results of the experiment showed that in this case as well the character of the change in the temperature of the lubricant in the oil bath of the reducer is the same. It should be concluded that the surge in temperature that occurred during tests of reducers at maximum load is explained by the rapid increase in the temperature of the layers of lubricant located near the rubbing pairs, by its melting, with subsequent heating of the more distant layers, accompanied by a certain decrease in temperature. In tests at a lower load level, heating of the lubricant occurred more slowly and more uniformly; therefore the temperature here gradually increased until a steady thermal regime was established.

As the temperature changes, the viscosity of the lubricant changes; the latter affects the magnitude of power losses in the reducer. As the lubricant temperature rises, the efficiency of the reducer increases. Figure 1 shows the change in the efficiency of the corresponding reducers over the course of the working day. As can be seen from the graphs in Fig. 1, the efficiency of the reducers changes more or less appreciably, as does the temperature, during the first hour of operation, and then changes little. Moreover, in comparison with the value of the efficiency under the established thermal regime, the difference in efficiency at the initial moment was 2–3%; 10–15 minutes after the installation was started, this difference is only about 1%, and then becomes quite insignificant.

Let us now turn to the question of the dependence of reducer efficiency on the magnitude of the load. In Fig. 1, efficiency graphs 1, 2, 3, and 4 were obtained on different reducers, each of which, during a prolonged wear test, operated at one definite load. From these graphs it would seem possible to conclude that the load does not affect the efficiency of reducers operating with grease lubrication. At the same time it is known that the efficiency of reducers operating with liquid lubrication decreases as the load is reduced [1]; this is explained by the fact that, when the load is reduced, the share of no-load losses increases relatively. To determine the influence of the magnitude of the load on the efficiency of a reducer operating with grease lubrication, the above-mentioned experiment of short-term tests (8 hours for each load) of one and the same reducer at different loads, corresponding to the loads of graphs 1, 2, 3, and 4 in Fig. 1, was used. The results of this experiment are represented by graphs 5, 6, 7, and 8 in Fig. 1. It is evident from them that in this case the efficiency of the reducer, even when operating with grease lubrication, decreases as the load is reduced. The close values of the efficiencies in graphs 1, 2, 3, and 4 are explained by the fact that the relatively large share of no-load losses at small loads was here compensated by the relatively greater value of the meshing efficiency (Fig. 4). The latter is explained

by the difference in the cleanliness of the tooth surfaces after wear under different loads [6]. In short-term tests of the same reducer under different loads, however, the cleanliness of the surface is practically the same; and with the same cleanliness of the tooth surfaces, as can be seen in Fig. 4 (the initial portions of the curves), the values of the meshing efficiency under different loads are close to one another. Hence, since the share of no-load losses relatively increases as the load decreases, the efficiency of the reducer correspondingly decreases.

In addition, over a wide range of loads an experiment was carried out to compare the efficiency values of reducers at a lubricant temperature corresponding to the steady-state thermal regime at each load, and the efficiency at a lubricant temperature identical for all loads. For this experiment the same reducers were also used that had previously been tested at the maximum load; here, however, the tests were conducted continuously, without changing the lubricant. In this experiment, at first a slow, gradual, stepwise increase of the load was performed. Moreover, the increase of the load to the next stage was carried out after the efficiency at the preceding stage had reached a constant value, i.e., after the establishment of a steady thermal regime. Then, in order to determine the efficiency at different loads and at close values of the lubricant temperature, a rapid stepwise decrease of the load was carried out. The results of this experiment are presented in Fig. 2. From this it is evident

Fig. 2. Change in reducer efficiency as a function of load.
Solid line—at the lubricant temperature corresponding to the steady-state thermal regime at each load; dashed line—at the lubricant temperature identical for all loads.

that the efficiency of the reducer increases when the load is increased. It is also seen that even with a rapid decrease of the load the efficiency of the reducer decreases; however, the efficiency value here, at all loads, is higher than it was initially during the gradual increase of the load. This is explained by the smaller values of no-load losses, owing to the higher temperature of the lubricant.

Let us now consider the difference in the efficiency values of the high-speed and low-speed stages of the reducers being tested. In Fig. 3 the efficiency values of these stages at different loads are shown as a function of the lubricant temperature in the oil bath of the reducers. The graphs of Fig. 3 co-

correspond to the gearboxes, the overall efficiencies of both stages of which are shown in curves 1, 2, 3, and 4 of Fig. 1. As can be seen from Fig. 3, the efficiency of the high-speed stage is higher at all loads than the efficiency of the low-speed stage. The latter is apparently explained by the fact that the operating regime of the high-speed stage is closer to fluid friction than that of the low-speed stage. This is also evidenced, in particular, by the values of the coefficients of friction in the gear meshes, given below in Fig. 4, which for the high-speed stage

Fig. 3. Change in the efficiency of the gearbox stages as a function of lubricant temperature.
Solid lines—efficiency curves of the low-speed stage; dashed lines—efficiency curves of the high-speed stage. The numbers on the curves denote the load values indicated in Fig. 1.

are lower at all loads than for the low-speed stage. However, Fig. 3 also shows that the absolute value of the difference in efficiency between the high-speed and low-speed stages of the gearboxes tested by us is small. As will be shown below, the high-speed stage has a higher efficiency of the gear mesh, but the low-speed stage has smaller no-load losses; these two factors compensate each other to a certain extent and bring the efficiencies of the stages closer together. Moreover, with an increase in the lubricant temperature in the gearbox oil bath, the efficiencies of the low-speed and high-speed stages become increasingly close. And, as can be seen from the curves in Fig. 3, at the temperature corresponding to the established thermal regime (Fig. 1), at all loads the difference in the efficiencies of the high-speed and low-speed stages becomes very small. The convergence of the efficiencies of the high-speed and low-speed stages as the lubricant temperature in the gearbox oil bath increases may be explained by the fact that the no-load losses of the high-speed stage change less with temperature than the no-load losses of the low-speed stage. This is evidenced by the no-load loss values given below, obtained in our experiments for the high-speed and low-speed stages at different loads and, correspondingly, at different lubricant temperatures.

Since at the lubricant temperature corresponding to the temperature value under steady-state thermal conditions, the efficiency values of the high-speed and low-speed stages practically almost do not differ (Fig. 3), then, without fear of introducing significant errors, the efficiency values of both stages under steady-state thermal conditions may be taken as equal in the calculations. It should be noted that if one compares the data of [1] on the efficiency of two-stage and single-stage enclosed transmissions operating with liquid oil, then there too one may conclude that the efficiencies of the reducer stages are close to one another.

During the course of the tests, together with wear of the gear wheels, the efficiency of the reducers changes. In order to exclude the influence of changes in lubricant temperature on the efficiency, we shall consider the efficiency under steady-state thermal conditions. This is all the more justified because the analysis carried out above of the change in reducer efficiency over the working day showed that, under the influence of changes in lubricant temperature, the efficiency changes more or less appreciably only during a short interval of time immediately following the start-up of the installation. Moreover, the lubricant temperature affects chiefly the magnitude of no-load losses, whereas tooth wear affects the efficiency of the gear mesh. Since tooth wear affects only the efficiency of the gear mesh, while losses in the bearings and for churning the lubricant practically do not change, the character of the change in the efficiency of the reducer or of its stages with wear of the teeth of the gear wheels completely coincides with the character of the change in the efficiency of the gear meshes. Therefore, in the present article we shall not dwell on the influence of tooth wear on the efficiency of the reducer or of its individual stages, especially since some information on this has been published by us earlier [2, 3]. Here we shall consider only the change in the efficiency of gear meshes with wear.

The efficiency of a gear mesh can be determined from the expression

\[ \eta_z = 1 - u, \tag{1} \]

where \(u\) is the relative magnitude of losses, i.e., the ratio of the torque expended on friction of the tooth profiles to the torque transmitted by the gear pair. In other words, like any mechanical coefficient of performance, the efficiency of a gear mesh is the ratio of the power delivered by the gear mesh to the power supplied to this mesh.

Usually authors, for example [7], when testing gear wheels on a closed installation, determine the efficiency of the gear mesh in a more simplified way, calculating the relative magnitude of losses \(u\) in expression (1) as the ratio of the torque \(M_z\), expended on friction in the gear mesh, to the torque \(M\) on the driving shaft of the gear transmission. Then the efficiency of the mesh is determined from the expression

\[ \eta_z = 1 - \frac{M_z}{M}. \tag{2} \]

When determining \(\eta_z\) from expression (2), it is not taken into account that part of the torque \(M\) before the mesh is spent on overcoming friction in the bearings of the driving shaft and on churning the lubricant by the driving gear wheel and other parts connected with the driving shaft. However, these losses, in comparison with the magnitudes of the torques on the shafts, are usually very small; therefore, as the analysis carried out by us has shown, the error in determining \(\eta_z\) from expression (2) is insignificant.

The magnitudes of the torques on the shafts of the tested reducers were determined from the expressions given in [4]. The friction torque in the mesh can be determined from the expression

\[ M_z = M_t - M_x - \Sigma M_p, \tag{3} \]

where \(M_t\) is the total loss torque in the reducer stage;
\(M_x\) is the no-load loss torque of the reducer stage;
\(\Sigma M_p\) is that part of the total friction torque in the bearings of the reducer stage which depends on the load.

The total loss torque \(M_t\) is determined as the difference between the torques on the driving and driven shafts of the stage, reduced to the rotational speed of the driving shaft. \(M_x\) was determined by measuring no-load losses during the tests. \(M_p\) for each bearing was determined separately, from experiments carried out on a special setup.

We shall not dwell on the values of \(\Sigma M_p\), first, because they are smaller than the corresponding values of \(M_x\), and, most importantly, they are practically independent either of the lubricant temperature or of the condition of the tooth surfaces under wear, and therefore have almost no effect on the change in the efficiency of the reducer or of the gear mesh. The value of the no-load losses, however, depends on the lubricant temperature. To compare \(M_x\) for the low-speed and high-speed stages, let us present the average values of these quantities, reduced to the rotational speed of the wheel shaft of the low-speed stage, which occurred in our tests at the lubricant temperature corresponding to the steady thermal regime for each load. In order of increasing loads from 1 to 4 (Fig. 3), the values of \(M_x\) were respectively: for the low-speed stage, 0.85; 0.75; 0.70; 0.65 kg·cm, and for the high-speed stage, 1.23; 1.19; 1.17; 1.15 kg·cm. From the values given it is clear that, owing to the higher rotational speed, the no-load losses in the high-speed stages of the tested reducers are greater than in the low-speed stages of these reducers. At the same time, the no-load losses of the high-speed stages vary less with changing load than the no-load losses of the low-speed stages. The latter is apparently explained by the viscosity characteristic of the lubricant, i.e., by the smaller change in lubricant viscosity with changing temperature in the contact zone of the gear-wheel teeth of the high-speed stages as the load changes, owing to the higher lubricant temperature in the contact zone of these stages as compared with the low-speed ones.

Graphs of the change in the efficiency \(\eta_z\) of the gear meshes of the tested reducers over the entire testing period for different loads are shown in Fig. 4. The corresponding values of the coefficient of friction \(f\) in the mesh are also plotted there. The latter were determined from the values of \(\eta_z\) using the expression

\[ f = \frac{1 - \eta_z}{\psi}. \tag{4} \]

The quantity \(\psi\) is a function of the geometrical parameters of the gear transmission. For involute gearing, the value of \(\psi\) can be determined, for example, from the formulas in [8]. It should be noted that, with wear, the shape of the tooth profiles changes and, consequently, the value of \(\psi\) changes. However, in order to make it possible to compare the obtained values of \(f\) with the data of other authors, the value of \(\psi\) was taken as unchanged in the calculations.

It is seen from the graphs in Fig. 4 that, in the course of wear, the efficiency of gear meshes first increases, while the coefficient of friction correspondingly decreases; then these quantities become almost constant. It should be noted that comparison of the graphs in Fig. 4 with the wear curves of the corresponding gear wheels given in [2, 3] shows that the strongest increase in the efficiency of the mesh and decrease in the coefficient of friction are observed in the first period of tooth wear of the gear wheels—the running-in period. During the period of established, uniform wear, the values \(\eta\) and \(f\) change little, even if scoring of the working surfaces of the teeth takes place. As shown in [6], the value of the coefficient of friction, and consequently also the efficiency of the mesh, changes during wear in accordance with the change in the cleanliness of the working surfaces of the teeth. As can be seen from Fig. 4, in the high-speed stage the efficiency of the mesh is always higher, and the coefficient of friction lower, than in the low-speed stage under the corresponding load. Since, moreover, for each gear pair the coefficient of friction decreased during the tests, by analogy with [7] it may be considered that the gear wheels tested by us operated under conditions of semi-fluid friction.

As noted by a number of authors, for example [7, 8], the value of the coefficient of friction in a gear mesh is almost independent of load. This conclusion is evidently based on the results of comparatively short-term tests, i.e., tests conducted with the same cleanliness of the working surfaces of the teeth. For example, in [7] it is stated that the values of the coefficients of friction reported there correspond to the initial period of operation of the experimental gear pairs, 5–7 hours after the beginning of the experiment. As can be seen from Fig. 4, in our experiments the values of the efficiency of gear meshes and of the coefficients of friction of a given stage under different loads are close to one another at the beginning of the tests, and then differ; moreover, the smaller the load, the higher the efficiency of the mesh and the lower the coefficient of friction after the running-in of the teeth. This is explained by the fact that at the beginning of the test the cleanliness of the working surfaces of the teeth of the gear wheels tested was approximately the same; subsequently, in the course of the tests, as shown in [6], the cleanliness of the tooth surfaces changes, and the smaller the load, the higher the cleanliness of the tooth surface during wear. Thus, the magnitude of the load affects the value of the coefficient of friction and the efficiency of the gear mesh through the change in the cleanliness of the working surfaces of the teeth during wear.

Many works are known on the experimental investigation of the values of coefficients of friction when lubricated with liquid oil, both directly on gear wheels and on rollers modeling the operation of gear-wheel teeth. Let us compare the results of these investigations with our experiments. Analyzing data from a number of investigators, obtained with lubrication by various oils and under different test conditions, covering the operating conditions of low-speed or medium-speed gear transmissions, the authors of [7] and [8] note that the values of the coefficients of friction usually lie within the limits from 0.05 to 0.1, more often from 0.05 to 0.08. As can be seen from Fig. 4, the values of the coefficients of friction obtained in our experiments also lie within these limits; at the beginning of the tests they are close to the upper limit, and at the end of the tests—to the lower limit. In [7] a graph is also given of the change in the coefficient of friction in a gear mesh during prolonged (330 hours) operation, for the case of lubrication with “machine T” oil. The value of the coefficient of friction on this graph at the end of the tests (\(f = 0.056\)) closely agrees with the results of our experiments (Fig. 4),

Figure annotations: vertical axes: \(f\), \(\eta_z\); horizontal axis: \(T\), hours.

Fig. 4. Change in the efficiency of gear meshes and in the coefficients of friction in the meshes over the entire duration of the tests.

Solid lines are graphs of the change in efficiency; dashed lines are graphs of the coefficients of friction. The numerals indicate the magnitude of the load; the subscripts indicate the name of the stage: T — low-speed, B — high-speed.

especially in the high-speed stage. It should be noted that the circumferential speed of the gear wheels in [7] was more than twice as high as in the high-speed stage in our experiments.

Thus, it may be concluded that with grease lubrication the efficiency of the reducer is no lower than the efficiency values given in the literature for liquid lubrication (for example, in [1] for a two-stage reducer with liquid lubrication, \(\eta = 0.95—0.96\) is indicated). The efficiency value changes comparatively little from the moment of start-up to the established thermal regime; consequently, grease lubrication can also be used in machines operating with frequent starts and stops, as well as with long interruptions during the working day. The values of the coefficients of friction in the mesh with grease lubrication are no higher than the values given in the literature for liquid lubrication. This is also confirmed in the experiments of [9]. The use of grease lubrication, as shown in [9], does not cause intensified tooth wear or a reduction in contact strength in comparison with liquid lubrication. Finally, the use of grease lubrication in many cases provides greater convenience in operation than lubrication of gear wheels with liquid oil.

LITERATURE

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

2. Yu. S. Semenov. Investigation of the wear of gear wheels of reducers of mining electric drills. Proceedings of the Conference on Problems of Calculation, Design, and Research 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 study of the wear of gear wheels of reducers of mining electric drills. Izv. TPI, Vol. 108, Investigation of Drilling Machines. Metallurgizdat, Sverdlovsk, 1959.

4. Yu. S. Semenov. A closed installation for testing gear transmissions under variable load. Izv. TPI, Vol. 96, Part 1, Publishing House of Tomsk University, 1959.

5. Hand-held electric drills ER-4, ER-5, ERP-5. Glavuglemash, Tomsk Electromechanical Plant named after V. V. Vakhrushev, Ugletekhizdat, Moscow, 1956.

6. Yu. S. Semenov, V. T. Gorbenko. Wear and cleanliness of the working surfaces of gear-wheel teeth. Izv. TPI, Vol. 114, Publishing House of Tomsk University, 1964.

7. G. K. Trubin. Contact fatigue of the teeth of spur gears. Mashgiz, Moscow, 1950.

8. A. I. Petrusevich. Gear transmissions. In: Machine Parts, ed. by N. S. Acherkan, Mashgiz, Moscow, 1954.

9. V. T. Gorbenko, S. I. Shubovich. On the wear of gear wheels of reducers of mining electric drills when operating with liquid lubrication. Izv. TPI, Vol. 147, Publishing House of Tomsk University, 1965.