Results of an Experimental Study of Wear in Gear Wheels of Mining Electric Drill Reducers
Abstract Generated abstract
This article reports laboratory tests on wear in the spur gear reducers of ER-5 mining electric drills, operated with grease lubrication under variable and constant loads representative of mine service. Fifteen two-stage reducers with different gear hardness combinations were tested on a closed rig, with wear measured by weighing and profile changes examined optically and with an involutometer. The experiments characterize efficiency, surface damage zones, pitting development, tooth-profile evolution, and wear rates under minimum, equivalent, maximum, and variable loading. The results suggest that pitting changes the mode of surface destruction but need not cause catastrophic wear in these reducers, while excessive hardness differences between mating gears increase running-in wear and should be avoided or offset by improved tooth-surface finishing.
Full Text
Results of an Experimental Study of Wear in Gear Wheels of Mining Electric Drill Reducers
Yu. S. Semenov
The present article is devoted to certain results of an experimental study that was carried out on the wear of gear wheels in the reducers of mining electric drills. The need for such a study arose because of the insufficiency of information on the operation of gears beyond the limits of tooth-surface pitting, especially under sharply varying load and with grease lubrication1, i.e., under the conditions in which the reducers of mining electric drills operate.
Test Conditions
The tests were carried out in the laboratory of the Department of Applied Mechanics of the Tomsk Polytechnic Institute on a closed test rig with loading according to the method proposed by Prof. V. N. Kudryavtsev [1].
The test object was a straight-tooth two-stage reducer of the most widely used hand-held electric drill ER-5 [2]. The layout of this reducer is shown in Fig. 1, a.
Fifteen specially manufactured reducers of two series were tested; they differed from one another in the hardness of the gears of the first stage. The gears of both stages were manufactured with teeth of a normal involute profile, without finishing operations: the pinions were made of 20Kh steel with subsequent carburizing and hardening; the wheels were made of 40Kh steel with subsequent hardening.
The hardness \((H_{R_c})\) of the working surfaces of the teeth is given in the table.
| Gear wheels | Series A, first stage | Series A, second stage | Series B, first stage | Series B, second stage |
|---|---|---|---|---|
| Pinion . . . . . . . . | 55—60 | 55—60 | 40—45 | 55—60 |
| Wheel . . . . . . . . | 40—45 | 30—35 | 40—45 | 30—35 |
The tests were carried out with grease lubrication (solidol M) and under a variable load, changing linearly within the limits from \(M_1\) to \(M_2\) (Fig. 1, b) at a frequency of 15 cycles per minute. The torque \(M_1\) corresponds to a contact stress on the wheel teeth \(\sigma_k^1\) of 4700 kg/cm² in the first stage and 6100 kg/cm² in the second stage; the torque \(M_2\) corresponds to 7600 kg/cm² in the first stage and 10,000 kg/cm² in the second stage.
Fig. 1. Kinematic diagram of the reducer (a) and graph of the variation of the load (b) of the ED-5 electric drill.
The frequency and limits of load variation in carrying out the experiments were adopted on the basis of average data from mine tests of electric drills [3]. In addition, for comparison, tests were conducted at constant loads: minimum \(M_1\), maximum \(M_2\), and equivalent \(M\). The magnitude of the equivalent load for \(T_{\mathrm{eq}} = T\) was calculated from the known relation [4], which for the linear loading regime (Fig. 1, b) has the form
\[ T_{\mathrm{eq}} = \frac{T}{4}\cdot \frac{n_{\mathrm{avg}}}{n} \left[ \frac{M_1}{M} + \frac{M_2}{M} \right] \left[ \left(\frac{M_1}{M}\right)^2 + \left(\frac{M_2}{M}\right)^2 \right], \]
where \(M_1\) is the minimum torque;
\(\phantom{\text{where }}M_2\) is the maximum torque;
\(\phantom{\text{where }}M\) is the equivalent torque;
\(\phantom{\text{where }}T_{\mathrm{eq}}\) is the time of action of the equivalent load;
\(\phantom{\text{where }}T\) is the time of action of the variable load;
¹ The stress \(\sigma_k\) was calculated by the Hertz formula for the case of meshing in a band under static loading and uniform distribution of the load over the entire length of the tooth.
$n$ — number of revolutions under the equivalent load;
$n_{\text{av}}$ — average number of revolutions under variable load.
The tests were carried out with the number of revolutions constant for all loads, $n = n_{\text{av}}$. The contact stresses under the equivalent load were, in the first stage, $\sigma_k = 6450\ \text{kg}/\text{cm}^2$; in the second, $\sigma_k = 8500\ \text{kg}/\text{cm}^2$. It should be noted that during the tests a concentration of load along the length of the tooth was revealed in the first stage, both wheels of which are arranged as cantilevers. Taking the latter into account, the magnitude of the contact stresses was: in the first stage, from 4700 to 11000 $\text{kg}/\text{cm}^2$; in the second stage, from 6100 to 11000 $\text{kg}/\text{cm}^2$.
The amount of tooth wear was determined by weighing 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 $\times 50$, and also additionally with the aid of an involutometer. The change in the appearance of the working surfaces of the teeth was established visually.
Some Test Results
- Experimental determination of the efficiency of one stage of a reducer operating with grease lubrication showed that it lies within the range 0.97–0.98, while the efficiency of the gear mesh, including losses in the bearings under load, reaches 0.987. This value of the efficiency corresponds to a coefficient of friction in the mesh (calculated by the usual method [5]) of 0.055–0.06. Similar values of the coefficient of friction are cited in the literature for gear pairs operating with oil lubrication [6].
The experiments showed that with grease lubrication the efficiency of a gear train changes with load less than with oil lubrication (Fig. 2). This phenomenon may be explained by the fact that, in the presence of grease lubrication, churning losses are less than with liquid oil, since the rotating gears carry along only that part of the lubricant which is directly adjacent to them. The tests also showed that the efficiency of the gear train after running-in does not decrease even with a large degree of wear of the working surfaces of the teeth. Thus, the use of grease lubrication does not cause any deterioration in the operation of the transmission from the standpoint of efficiency.
- Observations of the change in the appearance of the working surfaces of the teeth during their operation showed the presence of three characteristic zones: on the tooth tip, in the middle of the tooth at the pitch line (on both sides of it), and on the tooth root. On the driving pinion the height of the first zone is approximately 0.35, the height of the second zone 0.35, and of the third zone 0.3 of the total working height of the tooth.
(Fig. 3, a). On the driven gear these values are, respectively, 0.40, 0.32, and 0.28 (Fig. 3, b).
The condition of the surfaces of the above-mentioned zones changes depending on the duration of operation of the gear pairs, the magnitude of the load, and the ratio of the hardnesses of the mating wheels. Thus, for example, during the running-in process the first and third zones (at the tooth tip and root) have a smooth surface with small scratches in the direction of sliding; the second zone (the middle of the tooth) has a matte surface. At minimum load the condition of these zones remains almost unchanged, with no signs of characteristic—
Fig. 2. Graph of the change in efficiency of one reducer stage, including losses in bearings and in overcoming lubricant resistance:
1—minimum, 2—equivalent, 3—maximum load.
The dashed lines show the efficiencies of the installation reducers when operating with liquid oil.
—pitting over the entire duration of the tests. Under equivalent load, throughout the entire test period the surfaces of the first and third zones have the same appearance as under minimum load. On the surface of the second zone, near the pitch line, pitting appears over time; it then spreads over the entire surface of the second zone and does not cease throughout the entire test period. Under maximum load, the change in the surface condition before the appearance of pitting in the second zone proceeds in a manner analogous to the pattern described for the equivalent load; the difference consists only in the degree of wear. However, after the pitting has spread over the entire surface of the second zone, pitting appears in the first zone of the driving wheels and in the third zone of the driven gear wheels. Thus, for the maximum load, three stages of change in the appearance of the working surfaces of the teeth are characteristic: the first stage—before the onset of pitting in the second zone (for the—
the first stage is characterized by wear through abrasion, consisting of a running-in period and established uniform wear); the second stage includes the onset of pitting and its spread over the entire second zone; the third stage is the appearance and spread of pitting in the first zone of the driving gear wheels and the third zone of the driven gear wheels.
For equivalent load, the first two stages are characteristic, while for minimum load, chiefly only the first stage is characteristic.
- The nature of the change in the tooth profile (Fig. 3) in the different zones is different for each of the above stages of change in the condition of their working surfaces.
In the first stage, in all zones the profiles gradually shift into the body of the tooth, while remaining almost equidistant from the initial profile.
Fig. 3. Change of tooth profiles during wear under maximum load:
a—tooth of the driving gear; b—tooth of the driven gear; 1—first, 2—second, 3—third zones.
The magnitude of the displacement (wear) in this period is greater, the greater the load and the difference in hardness of the meshing gear wheels. The rate of displacement slows more and more with time.
In the second stage, the degree of wear in each zone is different. At the tooth tip (the first zone) the process proceeds similarly to the first stage, with an ever more decreasing intensity of wear. In the second zone at this stage, owing to the pitting that has occurred, the wear is greater than in the first zone; the third zone also wears appreciably more than the first. Thus, at this stage, in the second and third zones the profiles recede more deeply into the body of the tooth, while the first zone protrudes above the second and third. The pattern of change in the tooth profiles of the driving and driven gear wheels in the first and second stages is the same.
In the third stage, in contrast to the first two, the nature of the change in the tooth profiles of the driving and driven gear wheels is substantially different. At this stage, in the driving gear wheels (Fig. 3, a), owing to the spread of pitting into the first zone of the tooth tips, these are worn intensively; the tooth profiles
in all three zones become evened out, and subsequently the teeth wear comparatively uniformly over the entire working profile.
In the driven wheels (Fig. 3, б), at this stage wear in the first zone almost ceases; the second and third zones deepen still more in comparison with the first, and then, in all zones, wear assumes a slow, uniform character.
- The magnitudes of wear of the gear wheels are presented by the graphs in Figs. 4, 5, 6, and 7, according to which the magnitude of the load and the ratio of the hardnesses of the gear wheels affect both the overall magnitude of wear and the intensity of its increase. The difference in wear when these factors are varied is especially pronounced during the running-in period.
Fig. 4. Graph of wear of the first-stage pinions under:
1—variable; 2—minimum; 3—equivalent; 4—maximum loads.
Solid lines—driving pinions; dashed lines—driven pinions.
Thus, in the absence of an excessively large difference in the hardnesses of the meshing gear wheels (Figs. 4 and 5), tooth wear during this period is comparatively small, and its magnitude for all loads is close for both meshing gear wheels.
With a large difference in the hardnesses of the wheels of a gear pair (Figs. 6 and 7), however, the ratio of wear of the pinion and the wheel during the running-in period depends to a greater degree on the magnitude of the load. At minimum load the wear magnitudes of the pinion and the wheel are comparatively small and close to one another; at equivalent load the magnitude of wear of the wheel is considerably greater than the wear of the pin-
gear; at maximum load the difference in the wear values of the pinion and the wheel is very large. Under maximum load the pinion runs in very slowly and wears little—less than under the equivalent load. Because of its considerably lower hardness, the wheel wears very severely. Cases of complete wear, up to sharpening and rolling of the tooth tips, were observed only during the running-in period, without any traces of chipping. Wheel wear is especially great if it operates as the driver.
Fig. 5. Wear graph for first-stage wheels under variable (1), minimum (2), equivalent (3), and maximum (4) loads.
Solid lines—driving wheels; dashed lines—driven wheels.
In the second and third stages, the difference in the initial hardness of the meshing wheels of the gear pair affects the magnitude of their wear much less. The wear graphs of the wheels are, for the most part, curves of uniform (monotonic) wear, characterized by constancy of the wear conditions [7], although chipping occurs in this case, covering, under the equivalent load, the entire second zone, and under the maximum load extending to the first zone of the driving wheels or the third zone of the driven wheels.
The wear rate, characterized by the angle of inclination of the curves, increases with increasing load. In this case, the wear rate of wheels operating as drivers is usually higher than that of analogous wheels operating as driven wheels.
The wear curves of the gears also have a more or less uniform character; here, however, breaks are characteristic, with an increase in the angle of inclination of the curves. The increase in the angle of inclination of the curves here is associated with abrasion of the cemented layer. Moreover, the increase in the angle of inclination for the gears of the second stage under the equivalent load (Fig. 6), caused by local abrasion of the cemented layer during formation of a groove on the stem of a gear tooth at the point of meshing with the protruding head of a wheel tooth, after the surfaces had adapted to each other was again replaced by a slowing of the rate and by uniform wear.
Axis labels in the figure: tooth wear, mg; gear wear, mg; operating time, h; number of gear operating cycles.
Fig. 6. Wear graph of the second stage under variable (1), minimum (2), equivalent (3), and maximum (4) loads.
Solid lines—driving gears; dashed lines—driven gears.
In general, at all stages of operation of the gear pair of the first stage of series A, the wear of the wheel is somewhat greater than the wear of the gear; however, the values of wear per tooth are close, owing to the larger number of teeth on the wheel.
The meshing gear wheels of the first stage of series B (marked in Figs. 4 and 5 by primes) have, under all loads, similar wear values; however, the wear per tooth is greater for the gear than for the wheel, since it has a smaller number of teeth.
The total wear of the gear wheels of the first stage of both series over the entire test period is comparatively small and does not have a catastrophic character even when the third stage begins. This…
As for the gear wheels of the second stage, here, because of the large difference in hardness between the pinions and the wheels, the latter have a large amount of total wear, mainly on account of the running-in period; this applies especially to wheels that operated under maximum load. The pinions, in this case as well, generally have a small amount of total wear.
- Under variable load, the character of the wear process of the gear wheels of the first stage (Figs. 4 and 5), which have a smaller difference in the hardnesses of the mating teeth, is similar to the character of the
Fig. 7. Wear graph for second-stage wheels under variable (1), minimum (2), equivalent (3), and maximum (4) loads.
Solid lines—driving wheels; dashed lines—driven wheels.
wear process of analogous gear wheels under equivalent load. The wear magnitudes under variable load and the angles of inclination of the wear curves also lie in the region of the equivalent loads, with a slight shift toward the maximum loads.
For the gear wheels of the second stage, which have a large difference in the hardness of the surfaces of the mating teeth (Figs. 6 and 7), the character of the wear process under variable load approaches that of wear under maximum load. Here as well, during the running-in period of the first stage, the ratio between the wear magnitudes of the mating gear wheels is very large, although smaller than under maximum loads.
In the subsequent stages the rate of wear of the wheel also slows down. The spalling that formed in the second zone (the middle of the tooth) likewise then shifts, on the driving teeth, to the head, and on the driven teeth, to the tooth root; however, this occurs considerably more slowly than under maximum loads.
The tests carried out make it possible to conclude that, in the gear wheels of reducers for mining electric drills, spalling—while affecting the nature of the destruction of the working surfaces of the teeth and the nature of the change in their profiles—does not lead to catastrophic wear and is permissible under the operating conditions of the gear transmissions of mining electric drills. To avoid the greater overall wear of gear wheels caused chiefly by the running-in period, an excessively large difference in the hardness of the working surfaces of mating gear wheels should not be allowed. If gear pairs with a large difference in hardness of the mating teeth are used, it is necessary to improve the finish of their working surfaces.
REFERENCES
-
V. N. Kudryavtsev. Closed-loop installations for testing gear transmissions. Vestnik mashinostroeniya, No. 10, 1951.
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Hand-held electric drills ER-4, ER-5, ERP-5. Glavuglemash, Tomsk Electromechanical Plant named after V. V. Vakhrushev, Ugletekhizdat, Moscow, 1956.
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Problems of mechanization of mining operations (Collection of scientific papers No. 5). Moscow Scientific-Research Coal Institute, Ugletekhizdat, Moscow–Leningrad, 1952.
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Ya. G. Kistyán. Method for calculating gear meshing for strength. Mashgiz, 1954.
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Kh. F. Ketov and N. I. Kolchin. Theory of Mechanisms and Machines. Mashgiz, 1939.
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G. K. Trubin. Contact fatigue of teeth of spur gears. Mashgiz, 1950.
-
A. S. Pronikov. Wear and Durability of Machine Tools. Mashgiz, 1957.
Observed Misprints
| Page | Line | Printed | Should read | Fault of |
|---|---|---|---|---|
| 96 | Fig. 2 | \(n = 0.6\sqrt{\dfrac{Q \cdot p}{m \cdot S}} +\) | \(n = 0.6\sqrt{\dfrac{Q \cdot p}{m \cdot S}}.\) | author |
| 153 | 21 from top | \(t_k — 70\) mm, | \(t_k = 700\) mm, | printer |
| 160 | 12 from top | by wear | by wear | » |
| 182 | Fig. 2,a | the numerals 2 and 3 should be interchanged | the numerals 2 and 3 should be interchanged | author |
| 189 | 8 from top | by recording | being recorded | » |
| 198и | Formulas | \(q\) | \(q_n\) | » |
| 199 | (14) and (16a) | amplitude coefficient | shape coefficient | » |
| 200 | 14 from top | of the curve | » | |
| 205 | 12 from top | \(\sigma\) and \(\sigma\) | \(\sigma_b\) and \(\sigma_{\mathrm{g}}\) | » |
| 208 | 2 from top | \(d_{n1}=\) | \(D_{n1}=\) | » |
| 212 | 6 from bottom | \(\displaystyle = \frac{4.186}{t}\) | \(\displaystyle = \frac{4.186}{t_0}\) | » |
| 276 | 15 from bottom | of the second stage | of second-stage gears at | » |
| 287 | 14 from bottom | \(v_1,\ v_2\) and \(v_3\) | \(V_1,\ V_2\) and \(V_3\) | » |
| 287 | Formula (12) | \(\displaystyle \frac{2t_0 + t'_{\mathrm{sh}} + t'_{\mathrm{sh}}}{L}\) | \(\displaystyle \frac{2t_0 + t'_{\mathrm{sh}}}{L}\) | printer |
| 287 | Formula (13) | \(\displaystyle \frac{2t_0 + t''_{\mathrm{sh}}}{L}\) | \(\displaystyle \frac{2t_0 + t'_{\mathrm{sh}} + t''_{\mathrm{sh}}}{L}\) | author |
| 292 | 2 from top | (curve 1, | (curve \(1'\), | » |
Order 29
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Grease lubrication is used in reducers of mining electric drills for reasons of operational convenience. ↩