Paul Alciatore

10-23-2007, 12:50 AM

OK, so you are going to cut a gear. And it is perhaps 6 or 8 inches in diameter. DP does not matter, so assume 16 or 20 if you feel it makes any difference. Individual teeth or hobbed, my question is the same.

Just how much accuracy do you need in the dividing set-up? A common spec for a dividing head or rotary table is +/- 10 to +/- 30 seconds of arc. So lets use +/- 20 seconds which is about .0055 degrees. The sine of that angle is about 9.69 X 10^-5 or 0.0000969. Multiplying by a radius of 4 for the eight inch gear you get about 0.00039" or four tenths. So your error in the placement of the tooth or a segment of the tooth's surface if hobbing is going to be +/- 0.0004" or a total range of almost a full thousanth.

But it gets worse. Lets say you are going to use CNC. Now my rotary table with a 90:1 worm has four degrees on the handwheel, and each degree is divided into 60 minutes. The vernier is used to read down to 10 seconds. So there are 60 X 4 or 240 main (one minute) divisions on the wheel. If I replace the handwheel with a stepper for CNC, then I will have 200 steps per revolution. This seems to be a common way it is done, a 200 step stepper is directly coupled to the worm shaft. So I am now stepping in 1/50 degree steps (0.02 degree). This is about four times coarser than the manual indexing which allowed resolution to the 20 second level. Doing the calculation with the sine gives me an error of about +/- 0.0014" or a total positional range of almost three thousanths.

Now, the differences between the various numbered cutters for a single DP are measured in tenths. We are an order of magnitude larger in the positional errors. If I am hobbing, then the gear will first lag and then proceed the cutter by 0.0014". This will produce a variation, a wavyness in the finish of the teeth as the hob progresses across the face. Won't it?

It seems to me that the common solution of directly coupling a 200 step stepper to a worm is an order of magnitude too coarse for proper gear forming. Am I calculating incorrectly somewhere? Are the common CNC rotaries only used for very small gears, like under a half inch diameter? Or does everyone just ignore this problem? Does the tendency of a hob to follow the proper pitch win out over the stepper's attempt at positioning? Or am I just missing something?

And please don't talk about microstepping without a complete discussion of the non-linear errors and loss of torque that can occur with that mode of operation. I personally would not recommend it.

Just how much accuracy do you need in the dividing set-up? A common spec for a dividing head or rotary table is +/- 10 to +/- 30 seconds of arc. So lets use +/- 20 seconds which is about .0055 degrees. The sine of that angle is about 9.69 X 10^-5 or 0.0000969. Multiplying by a radius of 4 for the eight inch gear you get about 0.00039" or four tenths. So your error in the placement of the tooth or a segment of the tooth's surface if hobbing is going to be +/- 0.0004" or a total range of almost a full thousanth.

But it gets worse. Lets say you are going to use CNC. Now my rotary table with a 90:1 worm has four degrees on the handwheel, and each degree is divided into 60 minutes. The vernier is used to read down to 10 seconds. So there are 60 X 4 or 240 main (one minute) divisions on the wheel. If I replace the handwheel with a stepper for CNC, then I will have 200 steps per revolution. This seems to be a common way it is done, a 200 step stepper is directly coupled to the worm shaft. So I am now stepping in 1/50 degree steps (0.02 degree). This is about four times coarser than the manual indexing which allowed resolution to the 20 second level. Doing the calculation with the sine gives me an error of about +/- 0.0014" or a total positional range of almost three thousanths.

Now, the differences between the various numbered cutters for a single DP are measured in tenths. We are an order of magnitude larger in the positional errors. If I am hobbing, then the gear will first lag and then proceed the cutter by 0.0014". This will produce a variation, a wavyness in the finish of the teeth as the hob progresses across the face. Won't it?

It seems to me that the common solution of directly coupling a 200 step stepper to a worm is an order of magnitude too coarse for proper gear forming. Am I calculating incorrectly somewhere? Are the common CNC rotaries only used for very small gears, like under a half inch diameter? Or does everyone just ignore this problem? Does the tendency of a hob to follow the proper pitch win out over the stepper's attempt at positioning? Or am I just missing something?

And please don't talk about microstepping without a complete discussion of the non-linear errors and loss of torque that can occur with that mode of operation. I personally would not recommend it.