| Fig. 8. |
When a belt, in which the maximum and minimum tensions are respectively P and p ℔, drives a pulley, the torque exerted is (P − p)r ℔ ft., r being the radius of the pulley plus half the thickness of the belt. P and p may be measured directly by leading the belt round two freely hanging guide pulleys, one in the tight, the other in the slack part of the belt, and adjusting loads on them until a stable condition of running is obtained. In W. Froude’s belt dynamometer (see Proc. Inst. M.E., 1858) (fig. 8) the guide pulleys G1, G2 are carried upon an arm free to turn about the axis O. H is a pulley to guide the approaching and receding parts of the belt to and from the beam in parallel directions. Neglecting friction, the unbalanced torque acting on the beam is 4r {P − p} ℔ ft. If a force Q acting at R maintains equilibrium, QR/4 = (P − p)r = T. Q is supplied by a spring, the extensions of which are recorded on a drum driven proportionally to the angular displacement of the driving pulley; thus a work diagram is obtained. In the Farcot form the guide pulleys are attached to separate weighing levers placed horizontally below the apparatus. In a belt dynamometer built for the Franklin Institute from the designs of Tatham, the weighing levers are separate and arranged horizontally at the top of the apparatus. The weighing beam in the Hefner-Alteneck dynamometer is placed transversely to the belt (see Electrotechnischen Zeitschrift, 1881, 7). The force Q, usually measured by a spring, required to maintain the beam in its central position is proportional to (P − p). If the angle θ1 = θ2 = 120°, Q = (P − p) neglecting friction.
When a shaft is driven by means of gearing the driving torque is measured by the product of the resultant pressure P acting between the wheel teeth and the radius of the pitch circle of the wheel fixed to the shaft. Fig. 9, which has been reproduced from J. White’s A New Century of Inventions (Manchester, 1822), illustrates possibly the earliest application of this principle to dynamometry. The wheel D, keyed to the shaft overcoming the resistance to be measured, is driven from wheel N by two bevel wheels L, L, carried in a loose pulley K. The two shafts, though in a line, are independent. A torque applied to the shaft A can be transmitted to D, neglecting friction, without change only if the central pulley K is held from turning; the torque required to do this is twice the torque transmitted.
| Fig. 9. |
The torque acting on the armature of an electric motor is necessarily accompanied by an equal and opposite torque acting on the frame. If, therefore, the motor is mounted on a cradle free to turn about knife-edges, the reacting torque is the only torque tending to turn the cradle when it is in a vertical position, and may therefore be measured by adjusting weights to hold the cradle in a vertical position. The rate at which the motor is transmitting work is then T2πn / 550 H.P., where n is the revolutions per second of the armature.
See James Dredge, Electric Illumination, vol. ii. (London, 1885); W.W. Beaumont, “Dynamometers and Friction Brakes,” Proc. Inst.C.E. vol. xcv. (London, 1889); E. Brauer, “Über Bremsdynamometer and verwandte Kraftmesser,” Zeitschrift des Vereins deutscher Ingenieure (Berlin, 1888); J.J. Flather, Dynamometers and the Measurement of Power (New York, 1893).
(W. E. D.)
[1] H. Frahm, “Neue Untersuchungen über die dynamischen Vorgänge in den Wellenleitungen von Schiffsmaschinen mit besonderer Berücksichtigung der Resonanzschwingungen,” Zeitschrift des Vereins deutscher Ingenieure, 31st May 1902.