A Test Rig for Fatigue Fracture Testing of Worn Teeth
Abstract Generated abstract
The paper describes a laboratory pulsator rig developed for fatigue fracture testing of worn gear teeth in bending, a problem for which existing rigs for unworn teeth were inadequate because they used a fixed pressure angle. The design allows the tested tooth to be set at the required pressure angle for different wear conditions, applies a sinusoidally varying load at 18 Hz, permits adjustment of load amplitude and cycle asymmetry, and includes cycle counting and automatic shutdown at fracture or visible cracking. Static calibration using strain gauges on the elastic lever provides load measurement, and long-term tests on gear wheels indicated that the rig was serviceable, comparatively simple to maintain, and capable of producing acceptably accurate results.
Full Text
TEST RIG FOR FATIGUE FRACTURE TESTING OF WORN TEETH
I. F. Deryuga
(Presented by the scientific seminar of the Department of Applied Mechanics)
In recent years, much attention has been paid to fatigue tests of gear wheels for tooth fracture, since they are the most reliable and objective criterion for assessing the strength and durability of gear transmissions. Fatigue tests of teeth are acquiring still greater importance in connection with the recent tendency, in calculating teeth for bending, to take as the limiting stress the endurance limit of the tooth obtained as a result of full-scale tests of gear wheels [4, 5].
Of particular interest are tests for fatigue bending of worn teeth, since such tests are not described in the literature and no data of any kind are given.
Machines and rigs intended for testing new (unworn) teeth for fatigue fracture are described in works [1, 2, 3]; in these, the loading of the teeth was carried out at a constant pressure angle.
When teeth wear, the pressure angle changes; therefore, during tests of worn teeth having different degrees of wear, it is necessary each time to set the tooth being tested at the required pressure angle. This is difficult to accomplish on the rigs described in works [1, 2, 3].
To conduct comparative fatigue-bending tests of worn teeth, a pulsator-type rig was manufactured in the laboratory of the Department of Applied Mechanics of the Tomsk Polytechnic Institute, satisfying both the general requirements imposed on machines of this type and the specific requirements. The basic diagram of the pulsator is shown in Fig. 1.
The main elements of the diagram are: shaft 22 with eccentric 18; a cantilever-type loader made in the form of a flat elastic lever 16 with movable roller 17; shaft 10 with half-coupling 9; shaft 6 with experimental wheel 5 and half-coupling 8 and thrust bearing 2. The supports of shafts 6 and 10 are mounted on one rigid base, which made it possible to bore four holes for bearings 4, 7, 11, 12 in one setup and thereby ensure coaxiality of the shafts. Eccentric 18, rigidly fixed on shaft 22, is rotated by electric motor 24 through belt transmission 23. The eccentric, acting on roller 17, causes deflection of lever 16 with a maximum constant deflection of 1 cm. The force arising from the elastic deformation of parts 16, 10, 9, 8, 6
the force is transmitted to the tooth of the wheel being tested, 5. This force is directed toward the tooth profile at the pressure angle; it is constant in direction but variable in magnitude. Roller 17 can move along lever 16, changing the amplitude of the angular displacement of the lever and thereby making it possible to vary, over a wide range, the maximum value of the loading force.
Fig. 1. Schematic diagram of the pulsator
Within one cycle the load varies according to a sinusoidal law, as was confirmed by an oscillogram recorded on film, as well as by visual observation of the process on the oscilloscope screen. The frequency of cycle variation is 18 Hz.
Loading of the tooth being tested is carried out according to the scheme of a stop with simulated “gear wheel—rack” meshing for the instant of engagement when the load on the tooth is applied at the tooth tip.
Torque is transmitted from shaft 10 to shaft 6 by means of half-couplings 8 and 9 with annular grooves and four clamping bolts.
The setting of the tooth at the required pressure angle is achieved by rotating shaft 6 (and consequently wheel 5) after disconnecting shafts 6 and 10. For this purpose, on the cylindrical surface of coupling 9 there is a scale graduated in degrees.
With the aid of screw 1 and stop 2, possible backlash in the kinematic chain from link 18 to link 2 is eliminated, a preliminary load is created on the tooth, and any positive value of the cycle asymmetry coefficient in the range from 0 to 1 is ensured.
The number of tooth loading cycles during the experiments is recorded by revolution counter 20, connected to the eccentric shaft by means of flexible shaft 19.
For automatic switching off of the electric motor after tooth breakage has occurred, lever 15 is provided; at its end an adjustable stop 14 is placed. By changing, with a feeler gauge, the size of the gap between the tip of stop 14 and the “STOP” button of control panel 13,
it is possible to adjust the pulsator in accordance with a previously selected failure criterion (either complete tooth fracture or the appearance of a visible crack). The switch is actuated when the crack has developed sufficiently, owing to the change in stiffness of the tooth being tested and, ultimately, owing to the increased oscillation amplitude of lever 15.
Before testing begins, static calibration of the installation is performed. For this purpose, two wire strain gauges of ohmic resistance (one active, the other compensating) are bonded with BF-2 adhesive to the upper and lower faces of the ground lever 16 and are connected into a DC bridge. Two other gauges forming the bridge are provided by the amplifier circuit. A UT4-1 strain-gauge unit is used to supply the bridge and amplify the signal. The load measurement and recording circuit is shown in Fig. 2.
Fig. 2. Load measurement and recording circuit: 1—amplifier, 2—external milliammeter, 3—oscillograph, 4—oscillograph vibrator, 5—oscillograph screen, 6—elastic lever.
At first, for each position of roller 17 on lever 16 (at an interval of 1 cm), the readings of the external milliammeter are recorded at a maximum deflection of the lever equal to 1 cm. The lever is then rotated by 180 degrees from the right horizontal position to the left horizontal position so that each of the gauges is deformed in the same way as in the working position of the lever. With the same values of the arms, a compensating weight is selected, placed on a special suspension, which produces the same unbalance of the bridge as in the first case. A calibration graph is plotted from the calibration data.
To eliminate pickups and the interference and distortions associated with them, only shielded wires were used.
To protect the gauges from moisture, they were coated on top with “88” adhesive.
The design of the pulsator makes it possible, if necessary, to study the influence of the scale factor.
Using the pulsator described, long-term tests of gear wheels were carried out \((m = 2\ \text{mm};\ z = 28)\), which showed that this design is sufficiently serviceable and comparatively simple to maintain, and that the accuracy of the results obtained is quite acceptable.
REFERENCES
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G. S. Bocharov. Apparatus for testing gear-wheel teeth in bending, Vestnik mashinostroeniya, No. 10, 1953.
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V. I. Rudnitskii. Apparatus for fatigue testing of gear wheels, Zavodskaya laboratoriya, No. 11, 1957.
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K. I. Pantokhin. Selection of permissible stresses for calculating teeth in bending, taking into account the probability of non-failure and dispersion, in: Problems of the Quality and Strength of Gear Transmissions, Part 1, 1961.
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P. V. Semench. Refinement of the calculation of gear wheels for bending endurance, in: Problems of the Quality and Strength of Gear Transmissions, Part 2, 1961.