All materials which have a symmetrical cross section, such as round, square, octagonal, oval, or oblong, have the above line at their true centers, no matter which way they are bent. While the metal remains undisturbed at the center of any of the above sections, the rest of it undergoes a change; the inner portion, in the direction of bending, will contract and become thicker, and the outer portion will expand and become thinner.
Fig. 99.—Steps in Making Calipers.
Other conditions arise, however, to modify these rules. If the heat is unevenly distributed, or if the stock is not of a uniform thickness, the results will not be exactly as estimated. When a heavy ring is formed of oblong material and bent through its larger diameter, as shown in sketch A, [Fig. 100], and the product is to be finished to a uniform thickness, the expansion of the outer portion will make it necessary to use somewhat thicker material, to provide for the decrease of metal which will take place. The inner half, then too thick, could be reduced to the required size, but this operation always alters natural conditions of bending, and changes the general results. These conditions are not very noticeable and do not require special attention when small-sized materials are operated upon, but they must be observed when large oblong or square stock is formed into a ring requiring exact dimensions.
Fig. 100.—Calculations of Lengths for Rings.
In all cases of this kind, the required length must be established from the undisturbed center and the ends cut at an angle of 85 degrees. If the material is to be welded, it should be scarfed on opposite sides and lapped when bent.
When hoops or bands of flat or oblong material are bent, scarfed, and welded through the small diameter, then both scarfs should be formed on the same side while straight, and bent as shown at B, [Fig. 100]; the scarfs then will fit more readily than if they were formed on opposite sides. Sometimes, in instances of this kind, only one end is scarfed, and the piece is bent in a similar manner, with the unscarfed end on the outside and just lapping enough to cover the heel of the inner scarf.
Another form of ring requiring a calculation of the area as well as of the length is one of a wedge-shaped section, as shown at C, [Fig. 100]. Here the area of the required section is found and the material supplied with the proper thickness and area. The length also must be computed, then cut, scarfed, and welded, as previously explained; after this the ring may be drawn to the form desired.
The circumference of a circle may be found by multiplying its diameter by 3.1416 (π). (See tables, pages [205]-206.) For rings or bands the length of the center line, c, [Fig. 100], should be found. Example: If a equals 5 inches and b equals 2 inches, c will equal 7 inches, and the length of stock for the ring will be 7 × 3.1416 = 21.991 inches,—practically 22 inches. 31⁄7 may be used for the value of π instead of 3.1416.