Preliminary displacement as applied to the operation of a rubber conveyor belt
Abstract Generated abstract
This paper examines preliminary displacement and microslip in steel on conveyor rubber contacts as factors in calculating conveyor belt serviceability with respect to slipping on a driving pulley. Using magnified displacement measurements on rubber washer specimens under specified normal and shear loads, it records elastic recovery after removal of shear force, additional recovery after unloading normal pressure, residual displacement, and the transition from microdisplacement to microsliding. The experiments indicate that rubber permits much larger microdisplacements than metals and that microsliding can proceed at an approximately constant rate that increases with the excess of tractive force over the static displacement force. The author argues that, although microslip causes unavoidable energy loss and increased wear, a conveyor belt may tolerate substantially higher loading than would be inferred from a no microslip condition.
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PRELIMINARY DISPLACEMENT AS APPLIED TO THE OPERATION OF A RUBBER CONVEYOR BELT
I. R. Konyakhin
(Presented by the scientific seminar of the Department of Strength of Materials)
For calculating a conveyor belt in terms of its serviceability, determined by slipping along the rim of the driving pulley, it is necessary to know the magnitude of the preliminary displacement.
Experiments with rubber were carried out on an apparatus with a magnification of 125 times. When steel was displaced over rubber, the same phenomena were observed as when steel was displaced over various metals. The stiffness of the microdisplacement of rubber is 2000 times less than that of steel. During the experiments the following phenomena could be observed: elastic recovery when the displacing force was removed, a second recovery when the normal load was removed, and microslip after preliminary displacement.
The specimens of conveyor rubber were made in the form of a washer with a nominal working contact area of \(F = 1.7 \text{ cm}^2\).
During displacement the normal load was \(N = 10 \text{ kg}\), the maximum displacement force was \(P_{\max} = 5.5 \text{ kg}\); consequently, the coefficient of static friction was \(\mu_s = 0.55\).
Fig. 1. Displacement of steel over conveyor rubber.
In the graph shown in Fig. 1, the displacement of steel over conveyor rubber is presented.
In the graph of Fig. 1, \(OA\) is the primary displacement, \(AB\) is microslip; \(BC\) is the elastic recovery when the displacing force is removed; \(CD\) is the second recovery when the normal load is removed, observed only after preliminary displacement.
\(BC = S_v = 256 \text{ microns};\quad CD = S_t = 56 \text{ microns};\quad S_k = S_v + S_t = 312 \text{ microns}\) is the total elastic recovery, equal to the complete elastic preliminary displacement or, what is the same, to the elastic deformation of rubber in contac-
; \(S_{\text{sk}}\)—by sliding—\(248\ \text{mm}\). Rubber, unlike metals, shows a large microdisplacement before it passes into ordinary sliding.
Displacement was also carried out under a normal load \(N = 45\ \text{kg}\) by a force \(P = 18.5\ \text{kg}\). The displacement occurred without microsliding, since the displacement force, by its magnitude, was considerably less than the force of static friction. The total displacement was \(S = 1360\ \mu\). The elastic recovery upon removal of the displacing force was \(S_y = 930\ \mu\), and the second recovery upon unloading from the normal pressure was \(S_t = 312\ \mu\). The purely elastic microdisplacement was \(S_k = S_y + S_t = 1242\ \mu\); the residual displacement was \(S_{\text{res}} = 118\ \mu\).
As was shown in Fig. 1, microsliding begins at the end of the displacement. On contacting metallic surfaces this microsliding rapidly passes into rupture of contact, that is, into separation of the surfaces with their transition to ordinary relative sliding. On rubber, however, during microsliding the tractive force can be increased considerably without subsequent rupture; true, the rate of microsliding thereby increases greatly, while nevertheless remaining constant in magnitude for some time.
In one of the experiments, under a normal load \(N = 10\ \text{kg}\), a shearing force \(P = 7\ \text{kg}\) was applied, not by smoothly increasing it from zero, but at once, abruptly. After this, micromotion began, which continued for \(t = 200\) seconds. The results of the experiment are shown in Table 1.
Table 1
| \(t\), sec | 0 | 20 | 40 | 60 | 80 | 100 | 120 | 140 | 160 | 180 | 200 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(S\), \(\mu\) | 0 | 760 | 990 | 1170 | 1320 | 1680 | 1880 | 2200 | 2400 | 2560 | 2800 |
If, from the data of the table, one constructs a graph in the coordinates \(S\), \(\mu\); \(t\), sec, an inclined straight line is obtained. It does not quite pass through the origin, since during the rapid application of the displacing force the specimen had time to move somewhat forward.
Fig. 2. Dependence of the rate of microsliding of steel on rubber on the excess of the tractive force over the force of static displacement.
Line-
...ness of the graph indicates the constancy of the rate of micromotion. In this case it is equal to \(v = 13.8\ \mu/\mathrm{s}\).
This rate was obtained with a displacing force \(P = 7\ \mathrm{kg}\), while static displacement (Fig. 1) occurred under a force \(P = 5.5\ \mathrm{kg}\). Consequently, in this case there was an excess over the static force of \(q = 7 - 5.5 = 1.5\ \mathrm{kg}\). If this excess is increased, the rate of micromotion will also increase.
Further experiments were conducted with still greater excesses of the displacing force over the force of static displacement \(q\).
In Fig. 2, a graph has been constructed from these experimental results.
It is evident that the curve has an asymptote; that is, at some maximum excess of the tractive force over the force of static displacement, ordinary slipping will begin. It is possible that it will not occur so abruptly, but through an increase in the velocity.
Thus, a conveyor belt can be overloaded twofold compared with the case where there is no microslip. In this case, its wear will increase, but probably not very greatly. As for the energy loss due to microslip, it is, of course, impossible to avoid it.