Analysis

Cotters are used to fasten hubs to rods rather than shafts, the distinction between a rod and a shaft being that a rod takes its load in the direction of its length, and does not drive by rotation. A cotter, therefore, is nothing but a cross-pin of modified form, to take shearing and crushing stress in the direction of the axis of the rod, instead of perpendicular to it.

Referring to Fig. 72, one will see that the cotter is made long and thin - long, in order to get sufficient shearing area to resist shearing along lines A and B; thin, in order to cut as little cross-sectional area out of the body of the shaft as possible. The cotter itself tends to shear along the linos A and B, and crush along the surfaces K, G, and J. The socket tends to crush along the surfaces K and G. The rod end D tends to be sheared out along the lines C H and Q E, and also to be crushed along the surface J. The socket tends to be sheared along the lines V U and X Y.

The cotter is made taper on one side, thus enabling it to draw up the flange of the rod tightly against the head of the socket. This taper must not be great enough to permit easy "backing out" and loosening of the cotter under load or vibration in the rod. In responsible situations this cannot be safely guarded against except through some auxiliary locking device, such as lock nuts on the end of the cotter (Fig. 73).

Theory

Referring to Fig. 72, assume an axial load of P1 as shown. The successive equations of external force to internal strength are enumerated below, for the different actions that take place:

For shearing along lines A and B, w being the average width of cotter, and S, safe shearing stress of cotter,

P1, = 2TwS,. (106)

Fig. 72.

For crushing along surfaces K and G, Sc being least safe crushing stress, whether of cotter or socket,

P1.= T(D1- D)Sc,. (107)

For crushing along surface J, Se being least safe crushing stress, whether of cotter or socket,

P1= DTSC. (108)

For shearing along surfaces CH and QE, S, being safe shearing stress of rod end, and w, end of slot to end of rod,

P1 = 2w1DSs. (109)

For tension in rod end at section across slot, S, being safe tensile stress in rod end,

P1= (πD2 / 4 - TD)St. (110)

For tension in socket at section across slot, S, being safe ten-Bile stress in socket,

P1= [ n D1 2/ 4 - n D2 / 4 - T(D1 - D) ] St.. (Ill )

For shearing in socket along the lines VU and XY, S, being Bafe shearing stress in the Bocket, and w2 end of slot to end of socket.

P1 = 2w2 (D1- D) Ss (112).

The proportions of cotter and socket may be fixed to some extent by practical or as sumed conditions. The dimensions may then be tested by the above equations, that the safe working stresses may not be exceeded, the dimensions being then modified accordingly.

The steel of which both cotter and rod would ordinarily be made has range of working fiber stress as follows : Tension, 8,000 to 12,000 (lbs. per sq. in.) Compression, 10,000 to 16,000 (lbs. per sq. in.) Shear, 6,000 to 10,000 (lbs. per sq. in.) The socket, if made of cast iron, will be weak as regards tension, tendency to shear out at the end, and tendency to split. The uncertainty of cast iron to resist these is so great that the hub or socket must be very clumsy in order to have enough surplus strength. This is always a noticeable feature of the cotter type of fastening, and cannot well be avoided.

Fig. 73.

Practical Modification

The driving faces of the cotter are often made semicircular. This not only gives more shear-ing area at the sides of the slots, but makes the production of the slots easier in the shop. It also avoids the general objection to sharp corners - namely, a tendency to start cracks.

A practicable taper for cotters is ½ inch per foot. This will under ordinary circumstances prevent the Cotter from backing out under the action of the load. When set screws against the side of the cotter, or lock nuts are used, as in Fig. 73, the taper may be greater than this, perhaps as much as 1½ inches per foot.

In the common use of the cotter for holding the strap at the ends of connecting rods, the strap acts like a modified form of socket. This is shown in Figs. 73 and 74. Here, in addition to holding the strap and rod together lengthwise, it may be necessary to prevent their spreading, and for this purpose an auxiliary piece G with gib ends is used. The tendeucy without this extra piece is shown by the dotted lines in Fig. 74.

The general mechanical fault with cottered joints is that the action of the load, especially when it constantly reverses, as in pump piston rods, always tends to work the cotter loose. Vibration also tends to produce the same effect. Once this looseness is started in the joint, the cotter loses its pure crushing and shearing action, and begins to partake of the nature of a hammer, and pounds itself and its bearing surfaces out of their true shape. Instead of a collar on the rod, we often find a taper fit of the rod in the socket; and any looseness in this case is still worse, for the rod then has end play in the socket, and by its " shucking " back and forth tends to split open the socket.

Fig. 74.

The only answer to these objections is to provide a positive locking device, and take up any looseness the instant it appears. PROBLEMS ON KEYS, PINS, AND COTTERS.

1. Calculate the safe load in shear which can be carried on a key ½ inch wide, § inch thick, and 5 inches long. Assume Ss = 6,000.

2. Assuming the above key to be 3/16 inch in hub and 3/16 inch in shaft, test its proportions for crushing, at Sc = 16,000.

3. A gear CO inches in diameter has a load of 3,000 lbs. at the pitch line. The shaft is 4 inches in diameter, in a hub, 5 inches long; and the key is a standard gib key as given in the table. Test its proportions for shearing.

4. A piston rod 2 inches in diameter carries a cotter § inch thick, and has an axial load of 20,000 lbs. Calculate the average width of the cotter. Ss = 9,000.

5. Calculate fiber stress in rod in preceding problem at section through slot.

6. How far from the end of rod must the end of slot be?

7. Calculate the crushing fiber stresses on cotter, rod, and socket.

8. How far from the end of socket must the end of slot be, assuming the socket to be of steel ?