SQUARING THE CIRCLE
Part one by Graham Meek
SQUARING THE CIRCLE
Part one by Graham Meek
Given how the mistakes had happened things would have been a lot simpler if this was a whole number, or even 25 mm per revolution. Preliminary sketches soon showed that the 25 mm dial version, along the lines of the Myford S7 design. Was going to need a dial nearly as big as the Emco handwheel, which looked hideous, so no more work was done on this design. This was a pity because this would have made an ideal base for a 1” dial version for those readers with an Imperial versions of this lathe. The next design route was to make the new dial read 20 mm. This would mean a simple reduction with-in the dial which had a 19 to 20 ratio, or numbers thereof.
However, that was until I decided to check the actual carriage movement for one complete turn of the dial. I was a little surprised to find that the actual distance travelled was 18.97 mm. Given the countless thousands of jobs completed, many of them on a commercial basis. This error had never once scrapped a component. Even when the dial had been used to measure off lengths involving multiple turns. It did somewhat put a “stone in the ashes” as regards my simple 19 to 20 ratio though. Of course I could have just left it at that and used the 19 to 20 ratio, but the opportunity to get it right was beckoning, plus I do so love a challenge.
There was never going to be an easy way to incorporate all that I wanted to in the existing envelope. This was beginning to feel as though I was trying to “Square the Circle”, ie trying to do a very difficult or impossible task. Finally I did manage to square the circle as can be seen in Photo 2 (below).
This section gives the formula:
t = p/2 + e tan∅
Where, t = Tooth thickness, (at new PCD)
p = Pitch diameter of standard gear
e = Amount the outside diameter is increased over standard gear.
∅ = Pressure angle
Using the above formula it is possible to draw the required gear and those with AutoCad or similar will find it dead easy. These gears as they are drawn have no backlash. In order to create backlash, or play in any gear train. It is just a simple matter of cutting the teeth slightly deeper. As a very rough rule of thumb, every extra 0.025 mm in depth, gives 0.08 mm of backlash. In years gone by, the commercial gear cutters used to come with the depth of cut etched or stamped on the side, in the form of “D+f”. Where “f” is the extra increment to give the desired backlash. Sadly these days, even given we have the luxury of laser printing this information has been omitted on those new cutters I have purchased. One other point to make about the designed gear form; is that this is the correct tooth form for that particular gear. This is as close to a generated form, ie, hobbed form, that is is possible to get with a form tool cutter. The result of making these gears this way is that they are very smooth running.
However for this application it would be advantageous to have no, or as little backlash in the system as possible. To this end I worked to the basic Whole depth of the gear tooth, and just to make sure I cut one Delrin Idler Gear shallow in depth by 0.03 mm, while the other was cut to full depth. As it worked out the full depth gear gave no backlash, but I still have the larger one should any wear take place.
The next problem to raise its head was that there was no provision on the Emco or my own design of Dividing Head, Photo 3 (below), to cut 37 teeth. This was overcome by using AutoCad and the Array command to draw a new 37 hole indexing plate. Measuring off the coordinates on the drawing for each hole with reference to the indexing plate centre, a table of coordinates was prepared to drill the circle of holes on the FB 2. I hasten to add that my FB2 is not equipped with a Digital Readout. Some may think this method is fraught with errors but the resulting indexing plate did not show up any pitch errors and the Dividing Head indexing pin entered every hole as it should.
Modelengineeringwebsite.com
the only free and the only weekly magazine for model engineers.
Editor: David Carpenter