In vertical engines a want of balance at right angles to the line of the stroke is found to be most injurious, and in a horizontal engine a want of balance along the line of stroke. Both cannot be balanced at the same time, and hence for vertical engines we consider the former and for horizontal engines the latter. If the total weight concentrated at the crank pin = W, the total weight concentrated at the piston W1, the counterbalance weight = W2, the crank radius = r, and the distance of the centre of gravity of the counterbalance weight from the shaft centred, then to produce balance at right angles to the line of the stroke—

=

W2 × d = W x r.

Hence for vertical engines we use this rule to find W2 × d, so that their product is equal to W r. For horizontal engines, Prof. Unwin states that a usual rule is—

These rules are only approximate, for it is not absolutely correct to suppose the connecting-rod divided as in the above, nor ought we to take the centre of gravity of the counterbalance weight instead of more accurately its radius of gyration; but such a method is always adopted in work of this kind, the really accurate methods not giving results which differ sufficiently to make the difference at all practically appreciable.

That this latter statement is true will be recognised when we point out that the volume of the counterbalance weight required in order to fulfil the above conditions is often too great for practical adoption, and that the designer has to be satisfied with only balancing a part of the unbalanced masses. This we see when we know that the width of a counterbalance weight should not much exceed the thickness of the crank web, otherwise it will foul the connecting-rod end, nor should its distance from the shaft centre be greater than the most distant part of the connectingrod at the crank, otherwise it requires an increased clearance from the engine bed-plate.

EXAMPLES.

EX. 4. Design counterbalance weights for the crank shaft of the vertical engine, Ex. A (see Fig. 178 and Ex. A7, Section xxx.), to form a continuation of the crank webs, and to balance the crank pin, crank webs, and half weight of connecting-rod concentrated at the crank.

EX. 5. Design counterbalance weights for the crank shaft of the horizontal engine, Ex. B (see Fig. 196 and Ex. 27, Section xxx.),

to form a continuation of the crank webs, and to balance the crank pin and webs only.

(First calculate weight of pin and webs, then find weight required if at a distance equal to the crank radius. See how this weight will distribute in width and thickness, and if badly take a less or greater length for distance of centre of gravity of weight, and distribute again.)

APPENDIX.

MISCELLANEOUS EXAMPLES IN DRAWING AND DESIGN OF MACHINE PARTS, SELECTED FROM EXAMINATION PAPERS OF THE SCIENCE AND ART DEPARTMENT, AND VICTORIA UNIVERSITY.

EX. 1.-A foundation bolt of diameter d", with a square end, is secured by means of a cotter (see Fig. 131). Find the dimensions of the bolt and cotter, in terms of d, in order that the shearing stress on the cotter may be three-fourths, and the intensity of the bearing pressure on the cotter twice the tensional stress on the bolt. (S and A. H., 1886.)

EX. 2.-A wrought-iron shaft is required to transmit SO H.P. at 100 revolutions per minute. Draw one of the halves of a cast iron face-plate coupling for the shaft, and a bolt for connecting the two halves of the coupling together. Scale, full size. (Vict. Hon. B.Sc., 1889.)

EX. 3.-Determine the diameter of the 8 bolts of a flange coupling for a shaft 14" diam., which is subjected to torsion only, the diameter of the bolt circle being 23". Draw and dimension the coupling. (S. and A. H., 1887.) EX. 4.-Determine the necessary depth of the rectangular section of the guide bar of an engine, in order that the maximum stress in the material may not exceed 5 tons per square inch. Total pressure of steam on piston 25 tons, length of connecting-rod = twice stroke, width of guide bar 10". The greatest obliquity of the connecting rod may be taken to occur when the guide block is at the centre of the span of 4'. (S. and A. H., 1892.)

=

=

EX. 5.-Make working drawings of a connecting-rod end of the marine type (Fig. 189). Diameter of rod 24", of crank pin 4". (Vict. Hon. B. Sc., 1890.)

EX. 6.- Design a double chain-riveted (Fig. 142b) cover plate joint for boiler plates" thick, and discuss the proportion which the strength of the joint will bear to that of the plates. (Vict. Hon. B. Sc., 1890.)

EX. 7.-A tie rod for a roof is to be designed to stand a tension of 3 tons, with a stress of 4 tons per square inch. It is forked and fastened by a pin to the plate which is 1" thick. Design and draw the end of the rod-full size. (Vict. Hon. B. Sc., 1892.)

EX. 8.-Draw a stuffing box and gland for the upper cover of a vertical steam cylinder from the following data :-Piston-rod 3" diameter, cylinder cover 11" thick, gland 5" deep, gland bolts (two) 1" diameter. The gland to be of cast iron, and both gland and cylinder cover to be bushed with brass. (Vict. Hon. B. Sc., 1892.)

EX. 9.-Draw a cast-iron flange coupling to the following dimensions. Scale, half full size :

Diameter of shaft 3", diameter of boss of shaft 35", diameter of boss of coupling 7", diameter of bolt circle 10", six " diameter bolts, coupling 9" long, flanges 14" thick. Show suitable keys for attaching the flanges to the shafts. The bolt heads and nuts need not be sunk into the flanges. (Vict. U. Ord., 1892.)

EX. 10.—Make a full-size drawing of a knuckle joint for connecting two wrought-iron bars of 14" diameter. (Vict. U. Ord, 1892.)

EX. 11.-A steam engine has a piston of 100 per square inch area, stroke 1, connecting rod 3 long. The steam pressure during admission is 60 lbs. per square inch absolute, and the back pressure 5 lbs. per square inch, cut-off at stroke. Design and draw a crosshead for the engine to work between two parallel guide bars. (Vict. U. Hon., 1891.)

EX. 12-Draw a cast-iron pulley, with six curved arms, from the following data:--Extreme diameter 40", width of rim 9", thickness of rim at edge", diameter of shaft 4", thickness of boss 1", length of boss 6", section of arms at boss 24" x 11". Scale, 4. (Vict. U. Ord., 1891.)

EX. 13.-Design and draw the crank end of a connecting-rod of the marine type from the following data:-Diameter of steam cylinder 24", initial pressure of steam 100 lbs., diameter of crank pin 54", length of crank pin 7". Scale, 6" 1'. (Vict. U. Hon., 1888.)

EX. 14.-Two lengths of a mild steel rod of rectangular section, 7′′ × 1′′, are to be connected by means of a riveted butt joint with a cover plate on each side. Design and draw the joint and estimate its efficiency. (S. & A. H., 1893.)

INDEX OF PART II.

Connecting-rods, 282 to 286; length ECCENTRIC-ROLS, 295.