Determination of the weight of a flywheel according to Wittenbauer
Abstract Generated abstract
This paper presents Wittenbauer’s method for determining flywheel weight in crank and connecting rod mechanisms, contrasting it with the customary graphical calculation based on tangential crank-pin forces and an assumption of uniform angular velocity. It argues that the usual method is theoretically inconsistent because it neglects velocity fluctuations and the differing dynamic effects of rotating, reciprocating, oscillating, and connecting-rod masses. Drawing on Wittenbauer and Kölsch, the author outlines a teaching-oriented approach using diagrams of work and reduced masses, including graphical construction of integral curves in place of planimetry, to provide a more physically grounded yet comparably practical calculation procedure.
Full Text
V. G. Karpenko
DETERMINATION OF THE WEIGHT OF A FLYWHEEL ACCORDING TO WITTENBAUER.
The usual method of graphical calculation of the weight of a flywheel is based on determining the tangential force on the crank pin under the assumption of uniform angular velocity. The weight of the flywheel is calculated, for a given degree of nonuniformity, from the greatest excess area. But this calculation conceals a contradiction. Since there is nonuniformity in the rotation of the shaft, the velocity of the crank pin fluctuates from \(V_{\max}\) to \(V_{\min}\), and, consequently, the inertia forces of the rotating masses also change. On the other hand, no attention is paid to the distribution of the masses in the machine. In a crank-and-connecting-rod mechanism there are masses which execute rotary motion, there are masses which execute only oscillatory motion, and there are masses which execute neither complete rotary nor translatory motion and thus have a very variable influence on the motion of the machine. Meanwhile, in the usual method of calculation the weight of the connecting rod is added to the weight of the reciprocating parts of the machine, neglecting its [[unclear: role/influence]] on the motion, which is scientifically unfounded.
In the Wittenbauer method, both the variable influence of the moving masses and the change of velocities are taken into account; nevertheless, in its accuracy and scientific character it is no more complicated than the graphical method hitherto used for calculating the flywheel by tangential forces.
The considerations set forth above prompted the author to introduce the method of calculating the flywheel from diagrams of work and reduced masses into the teaching of Russian higher schools. To this end, using the works of Wittenbauer ) and Kölsch *), the author has provided exhaustive material for constructing the diagram of masses, or weights, and the diagram of work, replacing planimetry by the graphical construction of the integral curve.
) Z. d. V. d. Ing. 1896, S. 471.
*) O. Kölsch. Gleichgang u. Massenkräfte bei Fahr-u. Flugzeugmasch.