6 25.4 6 × 3 ------- = 6 ÷ ---- = ----- 25.4 3 25.4 ---- 3
The numerator and denominator of this fractional expression of the change-gear ratio are next multiplied by some trial number to determine the size of the gears. The first whole number by which 25.4 can be multiplied so as to get a whole number as the result is 5. Thus, 25.4 × 5 = 127; hence, one gear having 127 teeth is always used when cutting metric threads with an English lead-screw. The other gear required in this case has 90 teeth. Thus:
6 × 3 × 5 90 --------- = --- 25.4 × 5 127
Therefore, the following rule can be used to find the change gears for cutting metric pitches with an English lead-screw:
_Rule.--Place the lathe screw constant multiplied by the lead of the required thread in millimeters multiplied by 5, as the numerator of the fraction, and 127 as the denominator. The product of the numbers in the numerator equals the number of teeth for the spindle-stud gear, and 127 is the number of teeth for the lead-screw gear._
If the lathe has a metric pitch lead-screw, and a screw having a given number of threads per inch is to be cut, first find the "metric screw constant" of the lathe or the lead of thread in millimeters that would be cut with change gears of equal size on the lead-screw and spindle stud; then the method of determining the change gears is simply the reverse of the one already explained for cutting a metric thread with an English lead-screw.
_Rule.--To find the change gears for cutting English threads with a metric lead-screw, place 127 in the numerator and the threads per inch to be cut, multiplied by the metric screw constant multiplied by 5, in the denominator; 127 is the number of teeth on the spindle-stud gear and the product of the numbers in the denominator equals the number of teeth in the lead-screw gear._
=Quick Change-gear Type of Lathe.=--A type of lathe that is much used at the present time is shown in Fig. 30. This is known as the quick change-gear type, because it has a system of gearing which makes it unnecessary to remove the change gears and replace them with different sizes for cutting threads of various pitches. Changes of feed are also obtained by the same mechanism, but the feeding movement is transmitted to the carriage by the rod _R_, whereas the screw _S_{ 1}_ is used for screw cutting. As previously explained, the idea of using the screw exclusively for threading is to prevent it from being worn excessively, as it would be if continually used in place of rod _R_, for feeding the carriage when turning.