Manual of Gear Design: Helical and Spiral Gears, Volume III

AT TIMES, A WORM OR HELICAL GEAR WITH A SMALL NUMBER OF TEETH AND HIGH HELIX ANGLE IS REQUIRED TO MESH WITH ANOTHER HELICAL GEAR ON NON-PARALLEL AND NON-INTERSECTING AXES, AND GEAR GENERATING FACILITIES ARE NOT AVAILABLE TO CUT THE DRIVING MEMBER WITH THE HIGH HELIX ANGLE. IN SUCH CASES,THE PROPORTIONS OF THE GEARS WOULD BE CALCULATED AS A PAIR OF SPIRAL GEARS IN THE USUAL MANNER. THE DRIVING MEMBER WITH THE HIGH HELIX ANGLE MAY BE ROUGHED OUT BY ORDINARY THREAD-CUTTING METHODS. THE FORM WOULD THEN BE CORRECTED BY CHASING THE THREADS IN A LATHE WITH A STRAIGHT-SIDED TOOL SET TO THE LEAD ANGLE AT THE BASE RADIUS AND SET-OFF CENTER AN AMOUNT EQUAL TO THE BASE RADIUS OF THE DRIVER. THE DATA FOR FINISH CHASING SUCH A GEAR ARE DETERMINED AS FOLLOWS:
WHEN,
? n = NORMAL PRESSURE ANGLE AT R 1
R 1 = PITCH RADIUS OF DRIVER, INCHES
R b1 = BASE RADIUS AN DRIVER AND OFF-CENTER DISTANCE OF TOOL, INCHES
? 1 = HELIX ANGLE AT R 1
? 1 = LEAD ANGLE AT R 1
? b1 = LEAD ANGLE AT R b1 AND SETTING ANGLE OF TOOL
L 1 = LEAD OF DRIVER, INCHES
THEN,
? 1 = 90 - ? 1
COS ? b1 = COS ? n COS ? 1
| EXAMPLE: | N 1 = 4 | Nt = 40 | ? 1 = 80 | ? |