The Phenomenon of Preliminary Displacements When a Roller Starts from Rest
Abstract Generated abstract
This paper examines whether preliminary displacements, previously discussed for sliding friction, also occur in rolling friction when a roller starts from rest. The authors describe an apparatus with two steel cylindrical rollers between fixed and movable cast-iron plates, applying a gradually increasing horizontal force through a calibrated spring while measuring roller rotation by a mirror-and-scale method. Experiments under a specified load, with measurements averaged for motion in opposite directions, indicated that rollers undergo measurable preliminary angular displacements before regular motion begins. The study thus extends the phenomenon of preliminary displacement to friction of the second kind and provides experimental data relating driving force to roller rotation angle.
Full Text
The Phenomenon of Preliminary Displacements During the Starting Motion of a Roller
A. V. Verkhovskii
Professor, Doctor of Technical Sciences
V. M. Avraamov
Engineer
The phenomenon of preliminary displacements during starting from rest in the case of friction of the first kind (sliding friction) has already received some treatment in the literature [1, 2].
The authors of the present article set themselves the question of whether the phenomenon of preliminary displacements also occurs in the case of friction of the second kind (rolling friction).
To resolve this question, the authors constructed the apparatus shown in Fig. 1.
On a fixed cast-iron plate \((a)\) two cylindrical rollers \((b)\) were placed. A movable cast-iron plate \((c)\) was laid upon the rollers.
Fig. 1
The upper plate was loaded, by means of a special frame and weights not shown in the figure. The frame rested on the central point of the upper plate by means of a conical pin.
The upper plate and the rollers could be set in motion by means of a calibrated spring \((e)\).
The lower plate was brought into a horizontal position with the aid of screws \((n)\). In order to eliminate a possible error in the case of an inaccurate horizontal position of the lower plate, during the experiment the upper plate was first set in motion in one direction and then in the other, and the mean values were taken from the results obtained in the experiments.
The angles of rotation of the rollers during starting from rest were measured by the mirror-and-scale method, for which small mirrors were fastened to the ends of the rollers.
The experiments were carried out with rollers made of St. 5 steel, 40 mm in diameter, machined with a finishing tool. The surfaces of the cast-iron plates were scraped.
The experiment was carried out in the following manner. The upper cast-iron plate, with the aid of the frame, was loaded with a definite load \(Q\). After this, to it
by means of a calibrated spring \((e)\), a horizontal driving force \(P\) was applied. By stretching the spring, the horizontal force was gradually increased. At definite intervals, measurements were made of the angles of rotation of the rollers.
The results of the experiments confirmed the authors’ supposition that preliminary displacements occur in the case of friction of the second kind; these results are presented in the graph in Fig. 2 (the load \(Q\) was \(10\) kg).
Figure 2 shows a graph of the angles of rotation of the rollers as a function of the driving force.
Fig. 2
Along the abscissa axis of this graph the driving force is plotted in grams, and along the ordinate axis—the angle of rotation of the rollers in minutes.
The values of the force \(P\), as indicated above, were taken as the mean of two experiments when the upper plate was set in motion in one direction and in the other.
The angle of rotation of a roller was taken as the mean of the readings of the angles of rotation of both rollers.
LITERATURE
- A. V. Verkhovskii—Journal of Applied Physics, 1926, vol. III, nos. 3–4.
- V. D. Kuznetsov—Physics of the Solid State, vol. IV, Tomsk, 1947.