FIG. 27—Spiral 27—Spiral bevel and Zerol teeth can be ground after hardening 

Fig. 28—Zerol pinions of two different diameters are here generated to run with the same gear 
out some tolerance. With bevel gears in differential mechanisms, it is a sim-ple matter to adjust the backlash as desired by varying pinion position. In one known instance the change to bevel gears decreased the time for as-sembling the gears in an instrument from eight hours to one hour, and de-creased a measured error from 0.003 in. to 0.0015 in. Zerol bevel gears are being used with outstanding success in differential designs and in some cases have replaced straight bevel gears. Fig. 26 shows a hole for a taper pin through the hub of the gears. Pins and setscrews for holding gears on shafts should be avoided because of the danger of causing runout. In small gears, however, pins may have to be used ; and it is then of extreme impor-tance to control the fit between bore and shaft by the closest practical toler-ance.

 
pg 1222  
For small bevel gears which may be required to operate with zero backlash a natural, common-sense procedure produces satisfactory results. In the first place the gears are manufactured with the least possible amount of ec-centricity by taking special care in ma-chining the blanks and centering them on the arbors when cutting the teeth. Next the gears are assembled and ad-justed so as just not to be loose in any position. The tighter positions in the teeth are then eased down by rolling the gears together with a little mild fine-grain abrasive. With carefully made gears surprisingly little of this treatment is necessary to reach the con-dition where the gears rotate with no backlash and no discernible tightness in any position. Finally, the gears are disassembled, the abrasive is removed thoroughly, and the mechanism is re-assembled. 
    Another set of bevel gears of instrument  type is shown in Fig. 27. Here the teeth are Zerol, generated by a spiral cutter, although one has to look closely to see that they are not really straight. Such teeth can be generated very fast, especially when what is called the double-duplex method is used, meaning that in both gear and pinion the cutters work simultaneously on both sides of a tooth space. This kind of cutting usually requires spe-cial dimensions of the gear blanks, and the Gleason Works should be con-sulted. One gear and one pinion in the picture are placed so as to show the locating surfaces at their backs. The importance of adequate backing surfaces ground truly square with bores cannot be over-emphasized. Most gears are designed and cut ac-cording to standard methods. Special cases are always occurring, however. Fig. 28 shows an unusual arrangement of right-angle bevel gears in which pinions of two different diameters are meshed with the same ring gear. The teeth are Zerol ; and the narrow face width is favorable. Such jobs always require special calculations and spe-cial attention. Fig. 29 shows a miscellaneous group of bevel gears for instrument applica-tions. The largest diameter is about 4 in. Straight teeth, spiral teeth and Zerol teeth are all represented. The pair in the lower left center position are of bronze. All of the others are of steel. Those in the upper center and lower left have Zerol teeth, which are hardened and ground, and so will not wear under load like gears of softer material. It is naturally difficult to make fixed rules for the selection of materials, size, type of teeth and final finishing process. The manufacturer is always glad to give his advice when consulted and can usually make sug-gestions which result in improved re-sults and decreased cost. 

Durability Important Gears are designed for durability and for strength. It is obvious that teeth must be big enough not to break under the required load. Old text-books and handbooks dealt only with the strength of gear teeth ; but dura-bility is usually just as important. Ex-cept when the material is hardened steel, gears of a sufficient size to run without wearing out over a reasonable period of time at a given load and speed are almost always stronger than may be required to resist breakage. In some applications there must be no wear at all, if operation of the gears is to continue to be satisfactory. Gear specifications include the fol-lowing:

 
AMERICAN MACHINIST 
Instrument GEARS 1942 AM.

   

A. General Size Diameter Face width Cone distance Pitch angle (in bevel gears)

B. Description of Teeth Number Pitch Helix angle or spiral angle (straight teeth have 0 helix an-gle) Tooth form Pressure angle Depth

C. Material and Treatment

D. Finishing process The whole range of tooth size may be divided into four classifications ar-bitrarily as follows:

Diametral Pitch Classification I to 2 coarse pitch 2 2 to 8 large pitch 8 to 32 small pitch 32 and finer fine pitch

In small gears, like those for instrument use, it is convenient to think of diametral pitch as indicating the number of teeth in a gear of 1-in. diameter. In general pitch will vary with di-ameter and load. Loads are stated in terms of torque and diameter, or • in pounds tangen-tial to the pitch circle. Often load is reduced to pounds per inch of face width. Safe values depend on mate-rial, pitch, speed, accuracy and finish. Detailed analysis usually involves esti-mating the load carried on one tooth and the resulting surface pressures. Speed is given either as revolutions per minute or as feet per minute on the pitch circle. The speed at which gears are to operate must be consid-ered in the design, and frequently de-termines the type of gear. General designations of speed adopted by the inspection committee of the A.G.M.A. are worth listing: Feet per Minute 0 to 80 80 to 400 400 to 2,000 Over 2,000 Designation Low speed Commercial medium speed Commercial high speed Precision high speed This list is entirely arbitrary; but it serves to indicate the range of speeds covered by gearing. In some applications accuracy in gears and gear teeth is important even at low speed. Accuracy is always re-quired for satisfactory operation at high speeds. Inspection of accuracy 

     Fig. 29—Straight teeth, spiral teeth an bevel gears 
is applied to the following features: Pitch or spacing Profiles (pressure angle and curva-ture) Lengthwise direction (lead, spiral angle) and curvature Concentricity of teeth with bore or hub There are various types of checking devices in which dial micrometers reading in 1/10,000 in. are employed, and some in which recording instru-ments are used. Accuracy of pitch and concentricity can be indicated directly and by the same general methods in all kinds of gears. In spur gears and helical gears, where the dimensions are constant from end to end of a tooth, it is possible to check profiles and leads by direct-reading instruments. In bevel gears, however, the same kind of uniformity does not exist ; and inspec-tion is done mostly by running gears together in correct position on accurately graduated testing machines. General tolerances indicate linear errors at points on the tooth surfaces. Allowances in gears up, to say, 10-in. diameter run about as follows: Inspection Limits—Inches 0.001 to 0.002 0.0005 to 0.001 0.0002 to 0.0003 Classification Ordinary commercial Good commercial Precision Limits of 0.0001 to 0.0002 in. are sometimes obtainable, but not under usual manufacturing conditions. Naturally, the closer the limits the higher the cost. It is a mistake to demand higher accuracy than is required for a d Zerol teeth are shown in the precision pictured here given application. On the other hand, precision results can be obtained only by the necessary degree of accuracy. Diameter, number of teeth and pitch in gears are interrelated. In gen-eral, for given diameters, fewer teeth are stronger and cost less to cut. More teeth, however, may result in smoother motion and perhaps slightly greater durability. In straight-tooth bevel gears, for instance, 15/15 teeth are entirely satisfactory for many pur-poses ; but if precision of motion is especially desired, 30/30 teeth would be preferred. Note that in spur gears having approximately equivalent cross-sections the numbers of teeth would be 20/20 and 40/40, respectively. When the number of teeth is de-creased, the length of the tooth pro-file becomes greater in proportion to the diameter, and this makes smooth motion more difficult to obtain. Going in the other direction, after the number of teeth becomes sufficient to insure satisfactory precision, further in-crease in number does not bring fur-ther improvement, but makes cutting tools weaker and increases cost. The decrease in tooth size may also lead to danger of breakage. Design must always be based on knowledge and experience. General formulas and tables must be used with judgment. One designer may na-turally take more interest in gears than another. It is suggested, therefore, that such an individual in an engineer-ing office be encouraged to give spe-cial attention to gear design and be-come familiar with the best methods and practices. 
This concludes a series of three articles by Mr. Candee. 

OCTOBER 29, 1942 pg. 1223