LMS Mini Lathe Feed Rate - Vary Gears?

[homebrewed]

@homebrewed

Yes, I too found 116 gear combinations for 16TPI. However, there were more as my program only counts once for the condition where the gears at A=D AND B=C. Since I consider each axle's possible gear to be any of the 11 available there would be 11 events where A=D and for each of these there would be 11 events where B=C. For example, A=D=50 and B=C=30 (or A=D=80 and B=C=20.... etc etc) gives a total ratio of 1, but the lead screw has 16 TPI so the over all TPI is 16. That would meant that there would be 11x11 - 1 = 120 more possible event s (one was already counted in the 116) .

Of the 116 gears yielding 16TPI that were found, there are a large number of the ones in the 116 set where A=B AND C=D, but A is not equal to D. This occurs simply because the center two positions turn at the same rate (1 axle). So these are a simple case of redundant situations and these need to be noted as a form of duplicated gears. I must have just missed this situation in my code. I will have to check in to this some time.

My program had found a total of 12,321 while eliminating some duplicates. This is about 1/2 of the number you came up, 24,402, so I suspect that yours was counting duplicates or something or you used more gears than 11?

Is my thinking correct, if no duplicates are eliminated it would mean that there were 11*11*11*11 possible combinations, which is only 14,641 possibilities. That is for a pair of axle each with a possibility of 11 gears. Then that pair can generate 121 combinations. Add another axle and for each of the 121 from the first two axles there are 11x new combinations where the 3rd axle takes on values. Likewise, for the 4 axle's 11. I am not for sure how you would have gotten up to 24,402 unless you had more gears available.

So I just ran my program with the "elimination of duplicates" feature turn off. As expected, I got 14641 cases.

I will message you later about the code. Anyway, I am not for sure when I will be able to spend a lot of time studying it. There are a lot of things on the plate and my working on HM has been a diversion! (-:

The standard set of change gears for 7x lathes has 14 gears. They comprise the following tooth counts: 20, 20, 30, 35, 40, 45, 50, 55, 57, 60, 65, 80 & 80. The raw all-possible-combinations count included combinations like (20,40),(30,50) and (30,50),(20,40) which are functionally identical. This kind of combination is part of the 116 count for 16TPI. Probably many TPI's got similar contributions to their total count.

 

[B2]

I think you have the same set of gears that I had found, except I also had a 21 and you seem to have a 30. That is 20, 21, 35, 40, 45, 50, 55, 57, 60, 65, 80. (a count of 11 not counting any duplicates.) I had read that 20, 40, 80 had duplicates. (In you list I count 13, but 2 are duplicates so that make 11 unique gears, without the 21). My understanding from the LMS web site that the 21 and 57 were extra gears that could be purchased. Also, according to the threading table of page 30 of the manual https://littlemachineshop.com/images/gallery/ug/4100 Mini Lathe Users Guide - DISCONTINUED.pdf there is no 30 shown. While on page 9 it says
Change gears: 21, 30, 35, 40 (2), 45, 50, 55, 57, 60, and 65 teeth. But else where for the standard feed it says there are 20(2) and 80(2). So here it says there is a 30, but it is not used in the threading table!

Ironically, at the LMS Thread calculator, https://littlemachineshop.com/reference/change_gears.php, lists the gears and leaves out the 21 and the duplicate 40. "The normal set of change gears includes the following gears: 20, 20, 35, 40, 40, 45, 50, 55, 57, 60, 65, 80, and 80 teeth." So much inconsistancy. What is one to do!?

Also in the manual for the DRO there is a poor quality picture of the gears laid out on a table and it shows 11. One of them could be a 30 or a 21 it is impossible to say, or even if this picture has any meaning. .

So it seems if one can believe anything, a complete set might be : 20(2), 21, 30, 35, 40(2), 45, 50, 55, 57, 60, 65, 80(2). A total of 12 unique gears +3 duplicates. But all that is important is what the user has on hand. So for my workbook the total possible combinations (without removing duplicates) would be 12^4 = 20,736. I will add the 30 to my workbook and a user can remove what ever he does not have or add others if he has them.

So in my current workbook, I use the same set of unique of gears at every axle. In other words the computations are done as though one has 4 copies of each gear. This is how I got to the 12^4 combinations. Until I find time to modify the macro to check to make sure there are not too many copies of a gear is being use, it will just have to be up to the operator to realize the impossible cases.

 

[ChazzC]

Ironically, at the LMS Thread calculator, https://littlemachineshop.com/reference/change_gears.php, lists the gears and leaves out the 21 and the duplicate 40. "The normal set of change gears includes the following gears: 20, 20, 35, 40, 40, 45, 50, 55, 57, 60, 65, 80, and 80 teeth." So much inconsistancy. What is one to do!?

The LMS Calculator includes the 21T gear in the High-Torque Mini-Lathe setting (they include the 21T gear with their branded lathes) so you can just select that. Or, if you purchased the 21T gear for your other branded lathe you can add that to the Other Gears box:

 

[B2]

@ChazzC

Yes, this is the page I referenced in that posting via the URL. "The normal set..."

I change the number of gears in the workbook to 12, " 20(2), 21, 30, 35, 40(2), 45, 50, 55, 57, 60, 65, 80(2). A total of 12 unique gears +3 duplicates" and ran it. With the rules currently in the macro to eliminate some of the duplicates it yielded 17689 combinations as opposed to 12^4 = 20,736 when duplicates are not removed. The best that I can tell by a quick look is that only the 16TPI have duplicates that meet the condition that A=B AND C=D but there are quite a few of these.