METHODOLOGY FOR STUDYING DYNAMIC LOADS IN WORN SPUR GEARS

I. G. VOLKOV

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

A number of works, for example [1; 2], have been devoted to experimental studies of the dynamic loads of unworn spur gears. But in our experiments it did not appear possible to make full use of the experience accumulated in this area of research. When studying the dynamic processes of worn gears, a number of problems arise, caused by changes in the geometry of the tooth profile during wear and by the circumstance that, over the course of the experiment (up to a certain degree of wheel wear), it is necessary to carry out a number of measurements of the most important parameters without disassembling the reducer. The specific conditions of the experiment required the development of mandatory provisions of the research methodology, which briefly reduce to the following: the experiment is conducted without disassembling the reducer; measurement of dynamic forces is performed at a constant loading torque of the gear and circumferential meshing speed; at each measurement the sensors are calibrated; the power absorber of the stand creates a uniform load on the reducer; identical lubrication conditions are maintained throughout the experiment.

The experiment was carried out on a test stand, a description of which is given in [3]. We shall briefly mention that the stand operated according to an open circuit; as the power absorber, a direct-current generator was used, operating on a wire load rheostat.

Measurement circuit and installation of sensors.
The measurement of dynamic loads as a function of wear was based on the method of strain gauging.

The measurement circuit in Fig. 1 included, in sequence: a removable bridge made of wire strain gauges glued to the end faces of a tooth; a current-collecting device; a strain-gauge station of type UTCh-1; and an N-102 loop oscillograph.

Wire strain gauges with a base of 5 mm and an ohmic resistance \(R = 100\) ohms were used. The gauges were compactly placed on the end faces of the teeth of the driven wheel, two on each side, near the fillets, at an angle of \(10^\circ\) to the radial axis of symmetry of the tooth. To protect the gauges from destruction during wear, their upper part was lowered approximately 1 mm below the worn part of the tooth. All gauges were active, which ensured high sensitivity of the bridge with complete temperature compensation. Special importance was attached to moisture protection of the gauges under conditions of prolonged operation in an oil medium. We successfully

but a moisture-protective coating of epoxy resin with the addition of 10% hardener and 15% plasticizer was used.

The transducers were glued with BF-2, with obligatory polymerization after drying in air. After polymerization, creep of the transducers’ cement layer was practically absent.

A brush-type current-collecting device with silver rings of diameter $\varnothing 8\ \text{mm}$ and brushes made of a platinum-iridium alloy showed reliable operation with negligibly small signal distortions introduced by the transient resistances of the moving contacts.

Fig. 1. Arrangement of strain-gage mounting and block diagram of measurement

During each measurement the following were recorded on the oscillograph film: the magnitude of the force on the tooth under investigation during meshing, marks of the revolutions (which also served as marks of the beginning of meshing), and time marks with a frequency of 500 Hz. To measure the amount of wear, impressions were made from the investigated teeth of the wheels.

Before recording the process on film and after it, a mandatory check was made of the sensitivity of the strain gage by means of the electrical calibration signal available in the instrument.

Calibration

With wear, the geometry of the tooth profile changes continuously. Although a certain regularity is observed in this, manifested in the formation of three characteristic wear zones, for each stage of wear or type of wear failure the profile acquires a unique configuration; that is, the worn wheels are not interchangeable. Hence special conditions arise for calibrating the transducers: calibration in the very gearbox being tested, without disassembling it, at each measurement. Obviously, when calibrating the transducers one cannot exclude two-pair meshing, as is usually done by cutting off the teeth of the wheels adjacent to the one under investigation [1]. Therefore, for the two-pair zone, calibration was generally carried out after the force recordings and selectively, for checking, before the measurement. Calibration signals for 18–15 points along the length of meshing were recorded on the film and were marked on the degree scale. The angle of rotation of the wheels during meshing of the investigated pair of teeth was observed on the same scale.

Fig. 2. Calibration graph: I — beginning of meshing; II — beginning of one-pair meshing; III — end of one-pair meshing; IV — beginning of the 2nd zone of two-pair meshing; V — end of meshing.

The static calibration torque was produced by means of weights and a calibration lever fastened to the driving shaft. The driven shaft was locked by a special device with a screw feed, making it possible to rotate the wheels within the arc of engagement. During calibration, the characteristic points of changeover of contact were readily detected; the loading curves for them were plotted on the calibration graph in Fig. 2.

Measurement of Wear

The magnitude of wear was measured by the method of impressions taken from the teeth under study. The choice of material for the impressions is dictated by two basic requirements: minimal shrinkage and ease of use. To prepare the impressions we used a special mastic, the principal component of which is gutta-percha with beeswax. The shrinkage coefficient of the mastic is 1.05. At room temperature this is a resilient, elastic mass. When heated to 60°C it becomes plastic. High-quality impressions are obtained when the wheel is heated to 50°C. Forming in the space between the teeth, the impression copies with high accuracy not only the shape of the tooth profile but also records the condition of the worn surface. The impression clearly reveals the characteristic wear zones with microscopic irregularities.

The profiles of the impressions were projected onto the screen of a projector with a magnification of 20 times and traced with a sharply pointed pencil. The worn areas were then measured with a Coradi integrator, with subsequent recalculation to volumetric and weight wear.

It is more convenient to operate not with the absolute value of wear \(U\), but with the relative wear \(\Delta U\), which may be taken as equal to

\[ \Delta U = \frac{U}{m \cdot b}, \ \frac{\text{mg}}{\text{mm}^2}, \]

where \(m\) and \(b\) are, respectively, the module and the width of the wheel rim in mm.

The accuracy of wear measurement was determined mainly by the accuracy with which the worn areas were measured. The Coradi integrator estimated the area with an accuracy of up to 1%. An inaccuracy of the same order was allowed in tracing the profiles.

Taking into account the 20-fold enlargement of the profiles and, consequently, the 400-fold enlargement of the areas, the error of 2% must be reduced by a factor of 400, i.e., it will ultimately amount to

\[ \frac{1}{200}\%. \]

To eliminate the effect of differences in scale at different projector settings, all profiles of a single experiment were taken at one setting. If an impression is made from a new, unworn wheel and compared with subsequent ones, the effect of shrinkage will automatically be taken into account. It may be noted that the described method of measuring wear is not inferior, and even surpasses in accuracy, the method of direct measurement on analytical balances. At the same time, it has the indisputable advantage that it eliminates disassembly of the reducer and records the state of tooth wear for as long a period as desired.

Processing of Oscillograms

On the oscillograms, the maximum amplitude of the load was measured, corresponding to the full force on the tooth at the beginning of single-pair engagement. From the scale of the calibration graph, the magnitude of this force was determined, expressed in terms of the circumferential force of engagement.

The dynamic component of the force was determined as the difference between the total circumferential force \(P\) and the static component of this force \(P_c\).

\[ P_d = P - P_c . \]

The values of the dynamic coefficient \(K_d\) were calculated from the relation

\[ K_d = 1 + \frac{P_d}{P_c}. \]

In addition to the dynamic parameters of meshing, the oscillograms were used to determine, from the time marks, the frequency of load oscillations.

Conclusions

The developed methodology for studying the influence of wear on dynamic loads fully meets the stated objectives of the study. Tested by long-term experiments, it has shown the reliability and stability of measuring wear and dynamic loads. It can be recommended for laboratory investigations of the dynamics of worn spur-gear meshing.

Literature

1. A. I. Petrusevich, M. D. Genkin, V. K. Grinkevich, Dynamic Loads in Gear Transmissions with Spur Wheels. Academy of Sciences of the USSR, 1956.

2. V. A. Pestov. Experimental study of dynamic loads on the teeth of cylindrical spur gears. Factory Laboratory, No. 1, 1958.

3. I. G. Volkov. A test stand for testing the smoothness of transmission under gear wear. Proceedings of TPI, vol. 148, 1967.