TEST BENCH FOR EVALUATING TRANSMISSION SMOOTHNESS UNDER GEAR WEAR

I. G. Volkov

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

When gears wear, the geometry of the tooth profile changes substantially; manufacturing errors that excite angular oscillations of the wheels decrease. At the same time, the contact ratio decreases as wear progresses [2]. As a result, the quality of operation of the transmission during the process of tooth wear will not be stable.

There is a fairly well-established opinion that, when gears wear, the nonuniformity of rotation of the gears increases; however, direct studies of the influence of wear on the kinematics of gear transmissions apparently have not been carried out, since the few works in this area describe studies of the smoothness of gear meshing with unworn tooth profiles.

A preliminary analysis of indirect wear factors [1] and, in particular, of the wear of involute gears [2] shows that a noticeable deterioration in the smoothness of transmission operation is not to be expected up to a certain degree of wear.

For direct experimental measurements of the excess angular displacements of the driven member of a transmission as the gears wear, the author of the article designed a test bench, described below.

The principal feature of the test bench is that, on it, the degree of smoothness of the transmission under investigation is evaluated under load and at operating speeds. The kinematic diagram of the bench is shown in Fig. 1.

The driving motor 1, with a stator mounted in movable supports, is connected by cardan shaft 2 to the driving shaft of reducer 3. As the braking device, a direct-current generator 6 with load rheostat 7 is used. The generator is connected to the driven shaft of the reducer by an increasing two-stage V-belt transmission 5.

The angular-displacement sensor 9 of the driven gear is of the torsion-recording type with a strain-sensitive element. The role of the strain-sensitive element is performed by a flat spring, rigidly connected at one end to the rim of the flywheel and at the other to the shaft. The same spring “drives” the flywheel, which is freely mounted on the driven shaft of the reducer. When the mean angular velocity is reached, the sensor flywheel will rotate practically uniformly. The kinematic disturbances arising during meshing of the gears generate oscillations of the shaft and of the flat spring rigidly connected with it. Wire strain gauges are bonded to the spring; these convert the mechanical oscillations of the spring into corresponding electrical signals.

Fig. 1. Kinematic schematic of the test bench. 1 — drive motor; 2 — propeller shaft; 3 and 10 — induction pulse sensors; 4 — gearbox under test; 5 — V-belt drive; 6 — DC generator; 7 — load rheostat; 8 — excitation rheostat; 9 — sensor for angular oscillations of the wheel; 11 — current-collecting device; 12 — amplifier; 13 — high-pass filter; 14 — oscillograph; 15 — revolution counter (loading-cycle counter).

The parameters of the flywheel–spring system were selected so that its natural frequency, recorded on the oscillograph film, was much lower than the expected operating frequencies of the angular oscillations of the gear wheel. This makes it possible to record the process under study with practically no distortion. At the same time, careful embedding of the spring ends ensured high rigidity of the connection between the spring and the flywheel rim and the wheel shaft.

The measuring circuit of the angular-displacement transducer includes, in series: a measuring bridge made of wire strain gauges, a slip-ring device 11, a strain-gauge installation 12 of the UT-4 type, a high-pass filter 13, and an oscillograph 14 of the N102 type. For visual observation of the process, an electronic oscilloscope is connected.

The low-frequency filter eliminates all other oscillation signals of the system with frequencies below the meshing frequency of the pair of teeth. In this case, the oscillograph records the excess angular displacements of the driven gear wheel caused by kinematic disturbances during the meshing of each given pair of teeth.

The beginning of meshing of the tooth pair under investigation, at a gear ratio equal to unity, is detected from the spike of the curve of pulse sensor 10. For any other values of the gear ratio of the gear mesh, the beginning of meshing is observed at simultaneous emissions of the beams of pulse sensors 3 and 10. These same sensors served as revolution markers for the wheels. Using the time marks and the revolution marks, the average angular velocity of the moving links of the reducer was calculated.

Under the experimental conditions, all other factors, except wear, that affect transmission smoothness remained unchanged. Throughout the entire test (until complete wear of the wheels), a constant load was maintained on the tested reducer.

By adjusting the resistances of the load rheostat 7 and the rheostat of the excitation winding of generator 8, a definite operating mode was assigned to the driving motor, in which the reactive torque on the stator was balanced by the static torque on the load arm of the motor stator. The torque on the load arm was created by calibrated weights, by means of which the magnitude of the torque developed by the motor was quantitatively evaluated. In the event of sudden overloads due to random causes, a system for automatic shutdown of the motor was provided.

The structural layout of the bench, and the parameters of the drive and the power-absorption system, ensure uniform rotation of the driving shaft of the reducer. In particular, the motor power was specified above the maximum required drive power under wheel wear, which created a favorable thermal regime for the motor during prolonged and continuous operation of the bench. The double-jointed cardan shaft 2 compensates for angular-velocity oscillations arising as a result of possible assembly misalignment of the motor and reducer shafts. In addition, with such a connection the motor rotor acts as a flywheel for the reducer and, consequently, smooths the nonuniformity of rotation of the driving shaft of the reducer in the steady operating mode of the bench as a whole.

The parameters of the dynamic system drive–reducer excluded the possibility of resonance operating modes arising for the adopted range of operating wheel speeds.

On the bench described, it is possible to conduct experimental investigations of the dynamic loads on the wheel teeth as their wear progresses. With a sufficient number of collector rings on the slip-ring device, the recording of dynamic forces is carried out in parallel with the recording of excess angular displacements of the driven wheel.

In conclusion, it should be noted that, in creating the test bench, we took as a basis the method proposed by Prof. M. A. Skuridin for single-profile testing of gear transmissions at operating speeds and loads, using a torsiographic vibration sensor to measure the excess angular displacements of gear wheels [3].

REFERENCES

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

2. Yu. S. Semenov. Study of the wear of gear wheels in a mining electric-drill reducer. Proceedings of the Conference on Problems of Calculation, Design, and Research of Gear Transmissions and Flexible-Coupling Transmissions. Vol. III. Publishing House of the Odessa Polytechnic Institute, 1957.

3. M. A. Skuridin, L. A. Kudryavtsev. A method of comprehensive single-profile testing of gear wheels under operating loads and speeds. Izmeritel’naya Tekhnika, No. 7, 1961.