STUDY OF WEAR OF GEAR TEETH MADE OF VARIOUS MATERIALS

V. T. GORBENKO, V. V. BURKOV

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

In works [1—3] the results are given of a study of wear of the teeth of gear wheels of reducers for mining electric drills, and the nature of the change in the tooth profile under wear, the change in the geometric characteristics and service properties of the gear transmission are also shown. In [1—3], steel heat-treated gear wheels of reducers of mining electric drills of the ER-5 and ER-16 types, manufactured by the Tomsk Electromechanical Plant named after V. V. Vakhrushev, were subjected to testing. The tests were carried out with consistent grease (solidol M) and liquid lubricants (avtol AK-6, nigrol) under loads of different magnitude, including variable loads; the teeth of the gear wheels had different hardness ratios and different initial cleanliness of the working surfaces. All tests were carried out on a closed test rig.

For the purpose of comparing the magnitude and nature of wear and the change in the profile of the teeth of gear wheels made of different materials, we carried out tests with steel non-heat-treated, cast-iron, brass gear wheels and wheels made of silumin. In the tested gear pairs, pinions and wheels made both of the same and of different materials were meshed. The results of these tests are presented in the present article.

Spur gears with a module of 2 mm were subjected to testing; the number of teeth of the pinions was 17, of the wheels 28; the teeth were cut with a worm milling cutter; the teeth of all wheels were subjected to shaving and had a surface-finish class of ▽7, the pinions ▽6. The accuracy of the gear wheels corresponded to the 8th degree according to GOST 1643-56. The number of revolutions of the pinion was 830 rpm. The steel pinions were made of 20Kh material with a hardness of 160 HB; the wheels, of 40Kh steel with a hardness of ≃195 HB; the cast-iron pinions and wheels were made of SCh 15—32 material with a hardness of 168—170 HB; the brass pinions, of L68 material, HB≃120; the wheels, of LK 80—3 material (GOST 1019-47), HB≃95; the silumin wheels had a hardness of about 100 HB. The tests were carried out both on a closed test rig with loading by the method proposed by Prof. V. N. Kudryavtsev and described in work [3], and on an open test rig in order to accelerate the tests and to establish the influence of the type of stand on wear and on the change in the geometric profile of the teeth of gear wheels.

This rig, the general view of which is shown in the photograph in Fig. 1, contains motor 1 \((N = 2.8\ \text{kW},\ n = 1470\ \text{rpm})\), the stator of which can rotate on ball bearings in the supports of the copper—

ing reducer 2, the reducers under test 3 and 4, and the loading device 5. An air brake (a paddle wheel) was used as the loading device in the setup, as the simplest in design, requiring no maintenance and providing a stable load characteristic. To count the number of loading cycles of the gear wheels, a revolution counter 6 is used, connected by a flexible shaft to the shaft of the paddle wheel. On this setup, as on the closed-loop setup, two reducers were tested simultaneously, one of them operating as a speed-reducing transmission and the other as a speed-increasing transmission.

Fig. 1. Setup with an air brake (paddle wheel) for testing reducers

The required torque is ensured by selecting the dimensions of the paddle-wheel blades. For this purpose, before installing the reducers under test, the shafts of the paddle wheel and reducer 2 are connected by a special shaft, the setup is started, and the torque produced by the paddle wheel is determined from the torque at the motor stator. The procedure for preliminary determination of the dimensions of the paddle-wheel blades is given below.

The torque produced by the paddle wheel can be determined from the formula

\[ M = H_g \cdot S \cdot \frac{D}{2} \cdot k,\ \text{kgm}, \tag{1} \]

where \(H_g\) is the dynamic pressure, \(\text{kg}/\text{m}^2\);

\(S\) is the blade area, \(\text{m}^2\);

\(D\) is the diameter (through the center of gravity of the blades) of the paddle wheel, m;

\(k\) is the number of paddle-wheel blades.

The dynamic pressure, in turn, according to [4], is determined from the expression

\[ H_g = \rho \frac{v^2}{2} = \rho \frac{\left(\frac{\pi \cdot D \cdot n}{60}\right)^2}{2}, \ \text{kg}/\text{m}^2, \tag{2} \]

where \(\rho\) is the density of air \((\text{kg}\cdot\text{s}^2\cdot\text{m}^{-4})\);

\(v\) is the circumferential velocity of the blade’s center of gravity, m/s; and \(n\) is the number of revolutions per minute of the vane-wheel shaft.

With the air density under normal conditions \(\rho = 0.122\ \mathrm{kg\cdot s^2/m^4}\) and the vane-wheel shaft speed \(n = 508\) rpm, after substitution and transformation of equation (1) we obtain

\[ S = 0.0464 \frac{M}{D^3 \cdot k},\ \mathrm{m^2}. \tag{3} \]

The final dimensions of the blades were refined directly on the test setup. In doing so, by somewhat changing the dimensions or the arrangement of the blades, the specified value of the torque \(M\) was achieved. The magnitude of the latter was checked against the torque on the motor, \(M_d\), determined from the expression

\[ M_d = \frac{M}{i_2 \cdot \eta_2}, \tag{4} \]

where \(i_2 = 2.94\) is the gear ratio of reducer 2, and \(\eta_2\) is the efficiency of reducer 2 (on the basis of statistical data, as well as data from our tests, we took \(\eta_2 = 0.9\)). After this, the tested reducers are installed in place of the connecting shaft.

The loads at which the gear wheels were tested were determined on the basis of the following. As shown above, in works [2, 3] tests were carried out on thermally treated steel gear wheels of reducers for mining electric drills. To determine the effect of tooth pitting and wear of gear wheels on their service properties, the tests [2, 3] were carried out under loads exceeding by 1.89–2.52 times the allowable load calculated by the method of V. N. Kudryavtsev [5], without taking into account coefficients accounting for nonuniform distribution of the load across the width of the gear rim and the dynamic coefficient, i.e., \(K_{\mathrm{nr}} = K_d = 1\), but taking into account the operating mode of the transmission, \(k_e = 0.9\). The same overload factor was also adopted for determining the loading torque in testing unquenched steel, cast-iron, and brass gear wheels; i.e., dynamic similarity took place in testing the gear wheels of this series.

In determining the loading torque for unquenched steel and cast-iron wheels, the data and method presented by V. N. Kudryavtsev in work [4] were used. The torque on the gear wheel of the accelerating transmission calculated by this method was, for unquenched steel gear wheels, \(M_s = 128.4\ \mathrm{kg\,cm}\), and for cast-iron wheels, \(M_ch = 168\ \mathrm{kg/cm}\); the corresponding contact stresses were \(6000\ \mathrm{kg/cm^2}\) for steel wheels and \(4960\ \mathrm{kg/cm^2}\) for cast-iron wheels. (In the calculations, the modulus of elasticity was taken as \(E = 2.15 \cdot 10^6\ \mathrm{kg/cm^2}\) for steel and \(E = 1.1 \cdot 10^6\ \mathrm{kg/cm^2}\) for cast iron.)

Owing to the insufficiency of data in the domestic literature for calculating power gear transmissions made of nonferrous materials and alloys, in order to determine the magnitude of the load in testing gear wheels made of brass, we used the method set forth in work [6].

A preliminary comparison was made of the results of calculating allowable loads by the method of V. N. Kudryavtsev [5] and by the method [6] for hardened steel gears. The loading torque in testing brass wheels was \(M = 119.2\ \mathrm{kg\,cm}\) \((\sigma_k = 3650\ \mathrm{kg/cm^2}\) at \(E = 0.9 \cdot 10^6\ \mathrm{kg/cm^2})\).

The procedure for conducting the test did not differ from that which was applied in works [1, 2], i.e., during the tests the integral tooth wear was determined (change in the tooth profile due to wear), iz-

change in the condition of the working surface of the tooth. The tests were conducted mainly with consistent grease lubrication of the gear wheels (Solidol M). However, in order to determine the influence of the type of lubricant on wear and on the condition of the working surfaces of the teeth during wear, some experiments were also carried out with liquid lubrication (AK-6 automotive oil).

Figure 2 presents graphs of tooth wear for steel unhardened, cast-iron, and brass gear wheels. The graphs show that, as a rule, the wear of the teeth of the driving gear wheels, as also in [1—2], was greater than that of the driven ones, which is explained by the different character of friction on the driving and driven teeth. In all cases the teeth of the pinions had 2.3—1.4 times greater wear than the teeth of the mating wheels, whereas the transmission ratio is only 1.64.

Let us note some features in the character of the wear curves. Wear of the steel unhardened and cast-iron pinions occurred in steps; moreover, the steel pinions initially (during the running-in period) had increased wear compared with the steady-state period, while the wear of the cast-iron pinions during the running-in period, on the contrary, was less than in the steady-state period. The brass pinions, as well as all the wheels, had the same character of wear: after a short period of increased wear during running-in, a period of uniform (monotonic) wear followed until the end of the test. Pitting was observed on the working surfaces of the teeth of the driving pinion and the driven wheel in steel unhardened and brass gear wheels, on all cast-iron gear wheels, and on the teeth of silumin wheels.

Figure 4, a, b, c, d, and e shows the conjugate profiles of worn teeth of pinions (on the left) and wheels (on the right) of gear pairs made of various materials and operating under different loads (the profiles were taken on a projector). The character of the change in the geometric form of the tooth profiles during wear, for cast-iron (Fig. 4, c) and silumin (Fig. 4, d) wheels, did not differ from that described in [1, 2] for steel heat-treated gear wheels (Fig. 4, a). Particular features in the change of the profiles during wear were observed in steel unhardened gear wheels, where characteristic plastic flow of the metal occurred [5], when, owing to the different direction of the friction forces on the driving teeth along the pitch line, a depression was formed, and on the driven teeth—a ridge (Fig. 4, b).

Plastic flow of the metal with the formation of a depression and a ridge also occurred in brass pairs when they were tested on a closed-loop installation (during subsequent testing of these pairs on an open-loop installation, owing to significant bending deformation of the teeth, which is noted below, smoothing of the projection and ridge occurs—Fig. 4, g). This phenomenon was not observed in our tests in the remaining hardened, cast-iron, and silumin gear wheels.

Tests were carried out on several reducers whose gear wheels had a very large difference in hardness (for example, pinion of steel 20Kh, HRC-62, wheel of steel 40Kh, HB-195; pinion of steel 20Kh, HB-185—wheel of steel 40Kh, HRC-48; pinion of steel 20Kh, HRC-62—brass wheel HB-95; brass pinion HB-120—wheel of steel 40Kh, HRC-48, etc.). The load was set at 2—3 times the permissible load for the gear wheel with the lower hardness. The wear of the gear wheel that had low hardness, in comparison with the mating one, was very great in these experiments, up to almost complete abrasion in 4—6 hours of reducer operation. The profile of the worn tooth of the pinion or wheel, for example Fig. 4, e, differed little from the involute (the profile of the mating tooth with high hardness also had a deviation from the involute during the process

Fig. 2. Wear curves for the teeth of steel (S), cast-iron (Ch), and brass (L) gears. The subscript “Sh” refers to gears, the subscript “K” to wheels. Solid lines indicate driving gears and wheels; dashed lines indicate driven gears and wheels.

Fig. 3. Wear curves for the teeth of silumin wheels. Solid lines indicate driving wheels; dashed lines indicate driven wheels.

manufacturing). Thus, the nature of the change in tooth profiles under wear is determined by the direction of the friction forces, the tendency of the metal to flow, and the conjugacy.

In tests on an open setup with a lantern pinion, owing to the relatively large inertial masses and the short start-up time, impact application of the load occurred; as a result, in unhardened steel and brass gear wheels the bending strength of the teeth proved insufficient, and the teeth of both the wheels and the pinions acquired bending deformations, in some cases quite significant ones, with the driving teeth being more bent than the driven ones. On this basis it may be concluded that in such setups it is necessary to use special devices that would ensure a smoother start-up (for example, a friction coupling clutch). The shapes of the conjugate profile, as well as the condition of the working surfaces of the teeth under wear in tests on open and closed setups, proved to be identical.

Let us dwell separately on the experiments carried out with wheels made of silumin. The manufacturing technology and their design dimensions were the same as for wheels made of other materials, while their weight, compared with steel wheels, was 2.9 times less, with cast-iron wheels 2.5 times less, and with brass wheels 3.6 times less. The silumin wheels operated in mesh with unhardened steel and cast-iron pinions. Figure 3 shows the wear curves of these wheels. It should be noted here that, since in the literature we did not find a method for determining permissible loads for gear wheels made of silumin, the load for their testing was assigned by the method of successive loading, whereas gear wheels made of other materials were put into operation immediately at full load. Thus, for wheels \(A_1\) (Fig. 3) there were three load stages: \(M_I = 63.9\ \text{kg cm}\), duration 8 hours; \(M_{II} = 86.8\ \text{kg cm}\), duration 137 hours; and \(M_{III} = 133.8\ \text{kg cm}\), duration 55 hours. The corresponding contact stresses were: \(\sigma_{kI} = 2700\ \text{kg}/\text{cm}^2\), \(\sigma_{kII} = 3180\ \text{kg}/\text{cm}^2\), \(\sigma_{kIII} = 3980\ \text{kg}/\text{cm}^2\) for the silumin wheel and cast-iron pinion, and \(\sigma_{kII} = 3950\ \text{kg}/\text{cm}^2\), \(\sigma_{kIII} = 4370\ \text{kg}/\text{cm}^2\) for the silumin wheel and steel pinion (the modulus of elasticity for silumin was taken as \(E = 0.70 \cdot 10^6\ \text{kg}/\text{cm}^2\)). In the step-up reducer \(A_1\), the silumin wheel operated in mesh with a cast-iron pinion; in the step-down reducer, at the beginning of the test (55 hours), the silumin wheel also operated in mesh with a cast-iron pinion. After 55 hours of operation of the transmission, during the next disassembly, the end of the cast-iron pinion shaft broke off, and it was replaced by a new pinion made of 20Kh steel, not subjected to heat treatment, which initially caused increased wear of the mating wheel; this explains the jump in the wear curve of the driven wheel of reducer \(A_1\) in Fig. 3. Subsequently, as a result of the running-in of the pair, the wear again stabilized and the curve acquired a gently sloping character (monotonic wear). The tests were carried out with grease lubrication. Under the above loading regime, the integral wear of the silumin wheels was within the same limits as that of wheels made of other materials (the linear wear of the wheel teeth along the pitch-circle arc did not exceed 8–10%). The reducers \(A_1\) operated quite normally for 200 hours, after which the tests were discontinued.

The silumin wheels \(A_2\) (Fig. 3) operated in mesh with steel, non-heat-treated pinions; the torque on the wheel of the driving reducer was \(M = 161\ \text{kg cm}\) (\(\sigma_k = 4760\ \text{kg}/\text{cm}^2\)), i.e., was larg-

than in tests of steel unhardened and brass gear wheels. In this case the transmission operated for 60 hours; the tests were stopped because of the fracture of one of the teeth of the driving wheel (the tooth had a defect—a cavity in the form of a slag inclusion). The linear wear of the wheel teeth was 8%.

Fig. 4. Diagrams of worn teeth of pinions (left) and wheels (right):
a—steel hardened gear wheels (from work [2]); b—steel unhardened gear wheels; c—brass gear wheels; d—pinion—steel unhardened, wheel—silumin; e—profile of a heavily worn brass pinion (left), which worked in pair with a steel wheel made of steel 40Kh, HRC = 48, and of a steel wheel (right), which worked with a pinion made of steel 20Kh, HRC = 58.

Tests of these wheels were carried out alternately with grease and with liquid lubricants. The test results showed that changing the lubricant has practically no effect on tooth wear, while scoring on the working surfaces of the teeth decreased each time with grease and increased with liquid lubricant (AK-6 autol).

In Fig. 4, d the profiles of a worn mating pair are shown: a steel unhardened pinion (left) and a silumin wheel (right). It follows from the figure that the change in the profile of the silumin tooth has the same character as the profiles of wheel teeth made of 40Kh steel, having a hardness of 40–45 HRC (Fig. 4, a), or of cast iron (Fig. 4, c).

Preliminary tests of silumin wheels working in pair with steel unhardened and cast-iron pinions (the wheel material, moreover, was not of high quality—sand casting, slag inclusions) give grounds to suppose that such gear wheels can be used for individual transmissions in general machine building, and that in this way a reduction in the weight of the transmission can be achieved. For more specific recommendations, additional investigations are necessary.

References

1. Yu. S. Semenov. Study of the wear of gear wheels of mining electric-drill reducers. Proceedings of the conference on problems of calculating, designing, and studying gear transmissions with flexible coupling. Vol. III, Publishing House of the Odessa Polytechnic Institute, 1959.

2. Yu. S. Semenov, V. T. Gorbenko. Wear and cleanliness of the working surfaces of the teeth of gear wheels. Izvestiya TPI, vol. 114, Tomsk University Publishing House, 1964.

3. V. T. Gorbenko, S. I. Shubovich. On the wear of gear wheels of reducers of mining electric drills when operating with liquid lubrication. Izvestiya TPI, vol. 133, Tomsk University Publishing House, 1965.

4. V. L. Aleksandrov. Technical Hydromechanics, Gostekhizdat, 1946.

5. V. N. Kudryavtsev. Gear Transmissions, Mashgiz, 1957.

6. Calculation of gear wheels for service life taking into account the inertia forces of rotating masses. Underwood Clarence A. New formulas and charts help predict operating life of glars. Prod. Engug., 1962, 33, No. 10, 65–74. Express Information, Machine Parts, No. 32, 1962.