Manual of Gear Design: Spur and Internal Gears, Volume II

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WHEN PINIONS OF SMALL TOOTH NUMBERS ARE REQUIRED FOR SUCH APPLICATIONS AS MOTOR STARTING PINIONS OR LARGER REDUCTION RATIOS IN A SINGLE REDUCTION, UNDERCUT MAY BE MINIMIZED AND AN EFFECTIVE DRIVE OBTAINED BY ENLARGING THE DIAMETER OF THE PINION AND USING IT WITH A GEAR OF STANDARD PROPORTIONS. IN SUCH A CASE, THE CENTER DISTANCE WOULD BE INCREASED TO COMPENSATE FOR THE INCREASE IN THE DIAMETER OF THE PINION.
THE FOLLOWING TABLES GIVE THE TOOTH PROPORTIONS AND THE INCREASE IN CENTER DISTANCE FOR PINIONS OF FROM 5 TO 14 TEETH, BASED UPON THE BASIC RACK OF THE 20 FULL DEPTH INVOLUTE SYSTEM. THE FIRST TABLE GIVES THE RADII FOR 1 DP HOBBED PINIONS. THE SECOND TABLE GIVES THE INCREASE IN CENTER DISTANCE REQUIRED FOR VARIOUS COMBINATIONS. THE THIRD TABLE SHOWS THE CONTACT RATIO FOR THESE COMBINATIONS. THE FOURTH TABLE GIVES THE RADII FOR SHAPED PINIONS OF SEVERAL DIAMETRAL PITCHES. THESE DIMENSIONS MAKE NO ALLOWANCE FOR BACKLASH. TO INTRODUCE THE NECESSARY BACKLASH, THE MATING GEAR SHOULD BE CUT ENOUGH DEEPER TO SECURE IT, WHILE THE PINIONS SHOULD BE CUT AS SPECIFIED IN THE TABLES. THE FORMS OF THESE SMALL PINIONS ARE TOO SENSITIVE TO PERMIT ANY INCREASE IN THE DEPTH OF TOOTH WITHOUT INTRODUCING EXCESSIVE UNDERCUTTING.
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