The calculated lengths of iron crank-pins for the several cases by formulæ (1), (2), (7), and (8) are as follows: The calculated lengths for the long-stroke engines are too low to prevent excessive pressures. See "Pressures on the Crank-pins," below. The Strength of the Crank-pin is determined substantially as is that of the crank. In overhung cranks the load is usually assumed as carried at its extremity, and, equating its moment with that of the resistance of the pin, in which d = diameter of pin in inches, P = maximum load on the piston, t = the maximum allowable stress on a square inch of the metal. For iron it may be taken at 9000 lbs. For steel the diameters found by this formula may be reduced 10%. (Thurston.) Unwin gives the same formula in another form, viz.: the last form to be used when the ratio of length to diameter is assumed. For wrought iron, t = 6000 to 9000 lbs. per sq. in., d=0.0405 Pl3 for rigidity, and recommends that the diameter be calculated by both formulæ, and the largest result taken. The first is the same as Unwin's formula, with t taken at 9000 lbs. per sq. in. The second is based upon an arbitrary assumption of a deflection of 1-300 in, at the centre of pressure (one third of the length from the free end). Marks, calculating the diameter for rigidity, gives d = 0.066√ pl3Ð2 =0.945 4/(H.P.)/3 LN p = maximum steam-pressure in pounds per square inch, D = diameter of cylinder in inches, L= length of stroke in feet, N = number of single strokes per minute. He says there is no need of an investigation of the strength of a crank-pin, as the condition of rigidity gives a great excess of strength. Marks's formula is based upon the assumption that the whole load may be concentrated at the outer end, and cause a deflection of .01 inch at that point. It is serviceable, he says, for steel and for wrought iron alike. Using the average lengths of the crank-pins already found, we have the following for our six engines: Pressures on the Crank-pins.-If we take the mean pressure upon the crank-pin = mean pressure on piston, neglecting the effect of the vary. ing angle of the connecting-rod, we have the following, using the average lengths already found, and the diameters according to Unwin and Marks: The results show that the application of the formulæ for length and diameter of crank-pins give quite low pressures per square inch of projected area for the short-stroke high-speed engines of the larger sizes, but too high pressures for all the other engines. It is therefore evident that after calcu lating the dimensions of a crank-pin according to the formulæ given that the results should be modified, if necessary, to bring the pressure per square inch down to a reasonable figure. In order to bring the pressures down to 500 pounds per square inch, we divide the mean pressures by 500 to obtain the projected area, or product of length by diameter. Making = 1.5d for engines Nos. 1, 2, 4 and 6, the revised table for the six engines is as follows: Engine, No... Length of crank-pin, inches.. 1 2 3 4 5 6 3.15 3.15 9.86 8.37 17.12 13.30 2.10 2.10 7.34 5.58 12.40 8.87 Crosshead-pin or Wrist-pin.-Whitham says the bearing surface for the wrist-pin is found by the formula for crank-pin design. Seaton says the diameter at the middle must, of course, be sufficient to withstand the bending action, and generally from this cause ample surface is provided for good working; but in any case the area, calculated by multiplying the diameter of the journal by its length, should be such that the pressure does not exceed 1200 lbs. per sq. in., taking the maximum load on the piston as the total pressure on it, For small engines with the gudgeon shrunk into the jaws of the connect ing-rod, and working in brasses fitted into a recess in the piston-rod end and secured by a wrought-iron cap and two bolts, Seaton gives: Diameter of gudgeon = 1.25 X diam. of piston-rod, If the pressure on the section, as calculated by multiplying length by diameter, exceeds 1200 lbs. per sq. in., this length should be increased. J. B. Stanwood, in his "Ready Reference" book, gives for length of crosshead-pin 0.25 to 0.3 diam. of piston, and diam. = 0.18 to 0.2 diam. of piston. Since he gives for diam. of piston-rod 0.14 to 0.17 diam. of piston, his dimensions for diameter and length of crosshead-pin are about 1.25 and 1.8 diam. of piston-rod respectively. Taking the maximum allowable pressure at 1200 lbs. per sq. in. and making the length of the crosshead-pin = 4/3 of its diameter, we have d = VP+40,1 = √P +30, in which P = max. imum total load on piston in lbs., d = diam. and 7 = length of pin in inches. For the engines of our example we have: Which pressures are greater than the maximum allowed by Seaton. The Crank-arm.-The crank-arm is to be treated as a lever, so that if a is the thickness in direction paralel to the shaft-axis and b its breadth at a section x inches from the crank-pin centre, then, bending moment M at that section = Px, P being the thrust of the connecting-rod, and ƒ the safe strain per square inch, If a crank-arm were constructed so that b varied as V (as given by the above rule) it would be of such a curved form as to be inconvenient to manufacture, and consequently it is customary in practice to find the maximum value of b and draw tangent lines to the curve at the points; these lines are generally, for the same reason, tangential to the boss of the crankarm at the shaft. The shearing strain is the same throughout the crank-arm; and, conse. quently, is large compared with the bending strain close to the crank-pin ; and so it is not sufficient to provide there only for bending strains. The section at this point should be such that, in addition to what is given by the calculation from the bending moment, there is an extra square inch for every 8000 lbs. of thrust on the connecting rod (Seaton). The length of the boss h into which the shaft is fitted is from 0.75 to 1.0 of the diameter of the shaft D, and its thickness e must be calculated from the twisting strain PL. (L= length of crank.) For different values of length of boss h, the following values of thickness of boss e are given by Seaton: When h = D, then e 0.35 D; if steel, 0.3. h = 0.7 D. then e = 0.41 D, if steel, 0.34. The crank-eye or boss into which the pin is fitted should bear the same relation to the pin that the boss does to the shaft. The diameter of the shaft-end onto which the crank is fitted should be 1.1 X diameter of shaft. Thurston says: The empirical proportions adopted by builders will com. monly be found to fall well within the calculated safe margin. These proportions are, from the practice of successful designers, about as follows: For the wrought-iron crank. the hub is 1.75 to 1.8 times the least diameter of that part of the shaft carrying full load; the eye is 2.0 to 2.25 the diameter of the inserted portion of the pin, and their depths are, for the hub, 1.0 to 1.2 the diameter of shaft, and for the eye, 1.25 to 1.5 the diameter of pin. The web is made 0.7 to 0.75 the width of adjacent hub or eye, and is given a depth of 0.5 to 0.6 that of adjacent hub or eye. For the cast-iron crank the hub and eye are a little larger, ranging in diameter respectively from 1.8 to 2 and from 2 to 2.2 times the diameters of shaft and pin. The flanges are made at either end of nearly the full depth of hub or eye. Cast-iron has, however, fallen very generally into disuse. The crank-shaft is usually enlarged at the seat of the crank to about 1.1 its diameter at the journal. The size should be nicely adjusted to allow for the shrinkage or forcing on of the crank. A difference of diameter of one fifth of 1%, will usually suffice; and a common rule of practice gives an allowance of but one half of this, or .001. The formulæ given by different writers for crank-arms practically agree. since they all consider the crank as a beam loaded at one end and fixed at the other. The relation of breadth to thickness may vary according to the taste of the designer. Calculated dimensions for our six engines are as fol lows: The Shaft.-Twisting Resistance.-From the general formula π for torsion, we have: T= d3S = .19635d3S, whence d = 16 3 5.1T in which T= torsional moment in inch-pounds, d = diameter in inches, and S = the shearing resistance of the material in pounds per square inch. If a constant force P were applied to the crank-pin tangentially to its path, the work done per minute would be 2π in which L= length of crank in inches, and R revs. per min., and the mean twisting moment T = I.H.P. X 63,025. Therefore in which Fand a are factors that depend on the strength of the material and on the factor of safety. Taking Ŝ at 45,000 pounds per square inch for wrought iron, and at 60,000 for steel, we have, for simple twisting by a uniform tangential force, 5 6 8 10 a = 3.3 3.5 8.85 4.15 a = 3.0 3.18 3.5 3.77 Factor of safety = 5 6 8 10 Iron...... F= 35.7 42.8 57.1 71.4 Steel..... F= 26.8 32.1 42.8 53.5 Unwin, taking for safe working strength of wrought iron 9000 lbs., steel 13,500 lbs., and cast iron 4500 lbs., gives a 3.294 for wrought iron, 2.877 for steel, and 4.15 for cast iron. Thurston, for crank-axles of wrought iron, gives a 4.15 or more. Seaton says: For wrought iron, f, the safe strain per square inch, should not exceed 9000 lbs., and when the shafts are more than 10 inches diameter, 8000 lbs. Steel, when made from the ingot and of good materials, will admit of a stress of 12,000 lbs. for small shafts, and 10,000 lbs. for those above 10 inches diameter. The difference in the allowance between large and small shafts is to compensate for the defective material observable in the heart of large shafting, owing to the hammering failing to affect it. 3 I.H.P. The formula da assumes the tangential force to be uniform and that it is the only acting force. For engines, in which the tangential force varies with the angle between the crank and the connecting-rod, and with the variation in steam-pressure in the cylinder, and also is influenced by the inertia of the reciprocating parts, and in which also the shaft may be subjected to bending as well as torsion, the factor a must be increased, to provide for the maximum tangential force and for bending. Seaton gives the following table showing the relation between the maximum and mean twisting moments of engines working under various condi tions, the momentum of the moving parts being neglected, which is allow. able: 1. p. cranks opposite one another, and h.p. midway Seaton also gives the following rules for ordinary practice for ordinary h.p. 0.5, 1.p. 0.66 1.40 1.12 66 66 1.26 1.08 two-cylinder marine engines: Diameter of the tunnel-shafts = I.H.P I.H P. XF, or a R |