60

CHAPTER XV.

CRANKS, CRANKED SHAFTS, AND ECCENTRICS.

226. Strength and Proportions of Overhung Crank - Pins.-The dimensions of the overhung crank-pin are determined from two considerations. There is, first, the bending action on the pin, which is equal to PL, where P is the load on the pin and L the length of its journal. Then, there is the consideration that the intensity of the pressure on the journal must not exceed a certain amount, so as to ensure durability. If the pressure per square inch on the journal is too great, the lubricant is forced out and the journal wears rapidly. The bearing surface of a journal is taken as its diameter multiplied by its length. This is also called the projected area of the journal, because it is the area of the bearing surface "projected" on to a plane containing its axis. If P is the pressure on the journal in pounds per square inch of projected area, then pDLP, and therefore L

=

Р

PD

As stated above, the bending moment on the crank-pin journal is PL, that is,

P2 2pD

The moment of resistance of the journal to bending is

where ƒ is the greatest stress due to the bending moment.

P2

3.1416 D3f, which gives the result

2pD 32

(

From the formulæ L

and D=

1.5/P

we get

and

D

9

The following table gives values of K and C for various values of p and f

N

The smallest value of p given in the foregoing table, namely, 200 lbs. per square inch, would be taken for small high-speed engines, and the largest value, 900 lbs. per square inch, for large low-speed engines.

If it is desired to make the length of the crank-pin less than that given by the foregoing rules, the diameter must be increased so as to satisfy the equation pDL=

P. Let L="D, then npD2

For the eye at the crank-shaft end, L = CD, where C varies from 7 to 1.1. An average value of C is 9. T= KD, where K depends on C. Values of K for various values of C are given in the following table :

:

For the eye at the crank-pin end, l = cd, where c varies from 9 to 14, but it is generally about 1.2. tkd. Values of k for various values of c are given in the following table :

For the arm or web, the width H, measured at the centre of the shaft, may be taken equal to from 7D, to D1, where D1 =D + 2T. The width at the crank-pin end may be 7d, to d1, where d1 = d + 2t.

Having fixed upon the greatest width H of the arm, its thickness B is determined as follows:-First assume that the arm is subjected to bending only, the bending moment being equal to the twisting moment on the shaft. We may then take the resistance of the arm to bending equal to the resistance of the shaft to twisting, that is, BH2

3.1416

16

D3f

Having determined approximately, as above, the thickness of the arm, the distance m between the centre of the crank-pin and the centre line of the crank-arm is also determined approximately.

=

Let P be the greatest force which acts on the crank-pin in a direction at right angles to the crank-arm. This force produces a bending moment on the arm M = PR, and also a twisting moment M, Pm. Combining these we get the equivalent bending moment M2 = ¿M¿ + 1⁄2 √M¿2 + M,2. Now recalculate the thickness of the crank-arm from the equation BH2f = Me, where f is the safe tensile stress. In fixing upon the value off we use the factor of safety which was used in determining the diameter of the shaft.

The width of the key for securing the crank to the shaft does not generally exceed D for large cranks, and for small cranks it may be taken at 1D+1. The thickness of the key varies from 4 to 7 of its width.

228. Connection of Crank-Pin to Crank-Arm.-The part of the crankpin within the crank-arm may be parallel or slightly tapered. The most common method of securing the pin to the arm is by riveting, as shown in Fig. 453. The crank-arm is generally shrunk on to the pin, and if the part of the pin within the arm be parallel, as shown in Fig. 454, this is often quite sufficient to secure the pin. A good method is to make the

FIG. 453.

FIG. 454.

FIG. 455.

FIG. 456.

part of the pin within the crank parallel and slightly larger than the hole in the crank, and then force the pin into the crank by hydraulic pressure. With this method the difference between the diameters of the pin and the hole in the crank should be such that the pressure required to force the pin in is about 12 tons per inch of diameter. Sometimes the pin is kept from coming out by a cotter, as shown in Fig. 455, or by a nut screwed

on to the tail end of the pin, as shown in Fig. 456. The last two methods have the advantage that it is easier to withdraw the pin for renewal or repairs.

If the end of the rod which works on the crank pin is solid, the outer collar on the pin must be made separate from the pin. Two methods of attaching this loose collar to the pin are shown in Figs. 457 and 458.

FIG. 457.

FIG. 458.

229. Forged Cranked Shafts.—The form of cranked shaft shown in Figs. 459 and 460 is largely used for marine and other kinds of engines. The following rules are based on a large number of examples chiefly taken from marine engines. The letters refer to Figs. 459 and 460.

TaD, where a varies from 6 to 8. Average value of a =

L generally D.

Sometimes a hole is drilled through the crankpin, as shown, the diameter of the hole being about one-third the diameter of the pin.

7.

230 Locomotive Crank Axles.—The most common form of crank axle for locomotives with inside cylinders is represented in Figs. 461.

and 462, which show one half of the axle. The other half is exactly the same, except that the other crank is at right angles to the one

shown. The ends of the webs are frequently bevelled or rounded more or less at A, B, C, and E, as shown by dotted lines. These axles are now generally made of steel. The following table gives the dimensions of locomotive crank-axles taken from actual practice. D is the diameter of the steam-cylinders, and L the stroke of the pistons. The other letters refer to Figs. 461 and 462. All the dimensions are in inches.

On some railways it is the practice to hoop the crank-webs. An example of this, from a locomotive on the Midland Railway, is shown in Figs. 463 and 464. These hoops, which are shrunk on, are not added so much with a view to strengthening the cranks, but as a safeguard

against accident should a crank break.

FIG. 465.

For a similar reason a bolt is sometimes screwed into the crank-pin, as shown at (a), Fig. 465, which is also an example from a locomotive on the Midland Railway. Sometimes the bed for the hoop takes the form of a very shallow groove, as shown at (0), Fig. 465.