Re: Fw: 1948 9A Quick Change Gearbox analysis
john kling
Is the strange combinations of DPs only a feature of the work shop lathes? I wonder if the heavy (standard) lathes have a pure 16DP set up.
On Sunday, April 23, 2017 8:44 PM, "'Al Knack' arknack@... [SOUTHBENDLATHE]" wrote: Jon, What a marvelous write up. You put in a lot of work. Might want to pdf it and put it in the file section for future use. Al From: SOUTHBENDLATHE@... [mailto:SOUTHBENDLATHE@...] Sent: Sunday, April 23, 2017 2:05 PM To: SOUTHBENDLATHE@... Subject: [SOUTHBENDLATHE] Fw: 1948 9A Quick Change Gearbox analysis I wrote this long (and possibly terminally boring) analysis last year and posted it to Practical Machinist, but there’s probably more interest here.  I've had a lot of fun playing with my 1948 SB 9A's quick change (QC) gearbox and figuring out how it works, and thought I'd pass on what I've learned. I've also enjoyed playing with Onshape, and have been able to create a 3D representation of the end gears and gearbox. It's at <Animation  YouTube>. I think the 40 speed gearbox's design is extremely clever. Had I not disassembled it, I would have had a hard time figuring it out. The problem is some gears are pinned together, some are keyed to their shaft, and others are free to spin on their shaft  and there's no way to tell which is which just by looking. As with the rest of the lathe I've examined so far, the gearbox is constructed with a minimum of parts. Gears slide against each other with no thin washers between them, as I expected to find. The SB designers obviously thought them unnecessary, and 70 years have proven they were correct! Where clearance is required, it's cleverly achieved by varying the gear thickness. I learned a lot I didn't know about gears during this project. The first revelation was that SB uses gears of three different diametral pitches (DP) in the gear trains that connect the spindle to the lead screw. This photo of Paula Stevens' beautiful lathe (from Steve Wells' site at > shows the 20 DP and 18 DP end gears. The gearbox uses 16 DP gears. I added the tooth counts for the 20 DP gears. I had learned before that diametral pitch simply means number of teeth per inch of pitch diameter. Pitch diameter can't be measured directly, but overall diameter can. Diametral pitch approximately equals number of teeth plus two divided by overall diameter: DP ~= (T + 2) / D The first gears I measured were gearbox gears. The 20 tooth gear keyed to the lead screw measured about 1.375" diameter. According to the formula, that gave it a DP of 16. All the other gearbox gears worked out to be DP 16. I assumed all the gears were DP 16  not having seen the photo above  so I was confused when I measured the spindle gear. It was about 1.300" diameter and had 24 teeth. That gave a DP of (26 / 1.3) 20. I thought I'd measured or counted incorrectly and double checked. Nope, DP = 20. I also knew that spur gears that mesh have to have the same DP (as well as pressure angle). That meant the reversing gears and the inside gear on the "stud gear"  the 24 tooth one driven by the 32 tooth reversing idler  had to be 20 DP. The 32 tooth gears measured about 1.7" diameter. That works out to (34 / 1.7) 20 DP. At this point, I was confident all the end gears were DP 20. Then I measured the 1.22" diameter 20 tooth gear keyed to the 24 tooth stud gear and discovered it was (22 / 1.22) 18 DP. And the 4.55" diameter 80 tooth idler gear on the banjo also worked out to (82 / 4.55) 18 DP, as did the 40 and 56 tooth gears on the gearbox input shaft. It was probably at this point I checked the internet and found the photo above which confirmed my DP calculations. I'd love to know why the SB designers chose three different diametral pitches. I assume they had a very good reason for doing so. All the gears in this gear train have the same 14 1/2 degree pressure angle. The internet has several good articles on this parameter. My goto gear reference is Boston Gear's Gear Theory PDF at <http://www.bostongear.com/pdf/gear_theory.pdf>. The second revelation was about idler gears. Consider two meshed gears. It's intuitive they turn at different speeds relative to the ratio of their number of teeth. Here we have a 16 tooth gear driving a 32 tooth gear. (My reference says to call the smaller gear a pinion, but I'll just call them all gears.) In this case, the gear ratio is 16/32 or 32/16, depending on your point of view. Either way, the smaller gear makes two revolutions for each revolution of the larger gear. And we know from experience that the two gears turn in opposite directions. Now suppose a 16 tooth gear is placed between the two gears. The middle gear is an idler. Its only effects are to make the two outside gears rotate in the same direction, and change the distance between their centers. What wasn't obvious to me is that the number of teeth on the idler gear is immaterial. The ratio between the end gears remains the same irrespective of the number of teeth on the idler. It was also not obvious to me that any number of idler gears can be added to the chain, and each idler can have different numbers of teeth, all without affecting the overall gear ratio. Like this. The end gears still have a 2:1 ratio. If an odd number of idlers are interposed the end gears will rotate in the same direction. Understanding idlers was a key to my understanding of the gearbox operation. This photo shows the bottom view of my gearbox. (Larger version at http://i1084.photobucket.com/albums/...ps1od7cthc.png) There are actually two gearboxes arranged in series. They are connected together via the common double keyed shaft the tumblers slide on. The lefthand tumbler lever shifts the primary gearbox to one of five ratios: 2, 1, 1/2, 1/4, and 1/8 times the input shaft speed. The righthand tumbler lever shifts the secondary gearbox to one of eight ratios. Five primary ratios to eight secondary ratios gives 40 different possible overall ratios. Another eight ratios are available if the 20 tooth stud gear is replaced with the 40 tooth stud gear (which is stored on the outside of the 56 tooth gear.) The gearbox comprises several single gears and several gear clusters. Four clusters are made of a 16 tooth gear pinned to a 32 tooth gear. One cluster, called the cone gear, consists of eight gears keyed to the same shaft, with the four larger gears also pinned together. The input shaft has two two gear clusters mounted on it. Both gears A and B of cluster 1 are keyed to the shaft, while gears C and D of cluster 2 spin freely on it. On the intermediate shaft, idler 1, gears E and F of cluster 3, and gears G and H of cluster 4 all spin freely on the shaft. Gears I, J, K, L, M, N, O, and P of the cone gear cluster are all keyed to the shaft. In addition, cone gears M, N, O, and P are pinned together. Idlers 2 and 5 spin freely. Tumbler idlers 3 and 4 are double keyed to their common shaft. The tumbler levers slide left and right and move up and down. This allows idler 2 to mesh with idler 1, or gears E, F, G, or H. Idler 5 can mesh with any of the eight gears on the cone gear cluster. Cluster 1 is keyed to the input shaft, causing gears A and B to rotate at the same speed as the input shaft. Gear A (32T) drives idler 1 (16T) which rotates freely on its shaft at two times input shaft speed. Gear B (16T) drives gear E (32T) of cluster 3, causing gears E and F to rotate once for every two rotations of the input shaft. Gear F (16T) drives gear C (32T) of cluster 2, causing gears C and D to rotate once for every four rotations of the input shaft. Gear D (16T) drives gear G (32T) of cluster 4, causing gears G and H to rotate once for every eight revolutions of the input shaft. The lefthand tumbler shift lever can be positioned to mesh idler 2 with either idler 1, or gear E, F, G, or H. The speed plate identifies these as positions A through E. Idler 2 is in constant mesh with idler 3. Both idler 3 and idler 4 are double keyed to their common shaft and rotate at the same speed. Idler 4 is in constant mesh with idler 5. Idler 5 can be positioned to mesh with any of the eight cone gears, I through P. The speed plate doesn't label the righthand tumbler's positions, but I'll call the lefthand slot position 1. The five positions of the lefthand tumbler cause gear I to turn at 2, 1, 1/2, 1/4, or 1/8 times the input shaft speed. In position A, idler 2 meshes with idler 1. This puts idlers 1, 2, 3, 4, and 5 in a gear train that links gear A (32T) to gear I (16T), forming an overall gear ratio of 16:32, or 1:2. That causes gear I and the other cone gears to rotate twice for every rotation of the input shaft. The number of teeth on idlers 1, 2, 3, 4, and 5 have no bearing on the overall ratio. In position B, idler 2 meshes with gear E (32T). Gear E turns once for every two input shaft revolutions and drives gear I (16T) through idlers 2, 3, 4, and 5. The overall gear ratio of 1:1 causes gear I and the other cone gears to rotate once for each input shaft rotation. In position C, idler 2 meshes with gear F (16T). Gear F also turns once for every two input shaft revolutions and drives gear I (16T) through idlers 2, 3, 4, and 5. The overall gear ratio of 2:1 causes gear I and the other cone gears to rotate once for every two input shaft revolutions. In position D, idler 2 meshes with gear G (32T). Gear G turns once for every eight input shaft rotations and drives gear I (16T) through idlers 2, 3, 4, and 5. The overall gear ratio of 4:1 causes gear I and the other cone gears rotate once for every four input shaft rotations. In position E, idler 2 meshes with gear H (16T). Gear H turns once for every eight input shaft rotations and drives gear I (16T) through Idlers 2, 3, 4, and 5. The overall gear ratio of 8:1 causes gear I and the other cone gears to rotate once for every eight input shaft rotations. The output gear, 20T, is keyed to the lead screw. It meshes with gear P (28T), giving a gear ratio of 28:20, or 7:5. That means the output gear and lead screw always rotate at 7/5 times the cone gear speed. If the tumblers are set to position A1, then the cone gear rotates at 2 times the input shaft speed, which means the lead screw rotates at 14/5 the input shaft speed. The 24 tooth spindle gear drives the 24 tooth stud gear through one or two idlers, depending on the position of the reversing lever. That's 1:1. The 20 tooth gear is keyed to the same shaft as the 24 tooth gear and also turns at spindle speed. Thus, the gearbox input always turns at 20:56 or 5/14th spindle speed. The 80 tooth idler does not affect the 5/14 ratio. The overall ratio of spindle speed to lead screw speed is the combination of the ratio of spindle speed to gearbox input speed to cone gear speed to lead screw speed. This is determined by multiplying the three ratios: Spindle to Gearbox Input = 20:56 Gearbox input to Cone Gear = 32:16 (in position A1) to 2:28 (in position E8) Cone Gear to Lead Screw = 28:20 This gives lead screw to spindle ratios of 20/56 * 32/16 * 28/20 = 17920/17920 = 1/1 to 20/56 * 2/28 * 28/20 = 2240/31360 = 114/3136 = 7/196 With the gearbox tumblers set to position A1, the lead screw turns at (32/16 * 28/20 = 896/320 = 14/5 times the input shaft speed, and the input shaft turns at 5/14 times the spindle speed. The overall ratio is 14/5 * 5/14 or 1:1. Since the lead screw has 8 threads per inch, the saddle will move one inch in 8 turns of the spindle, cutting 8 threads per inch, just as the table says. In position A2, the lead screw turns at 20/56 * 32/18 * 28/20 = 56/63 times spindle speed (or about 0.8889x). That would cut 63/56 * 8 = 9 threads per inch. In position A3, the lead screw turns at 20/56 * 32/20 * 28/20 = 28/35 times spindle speed (or exactly 0.8x). That would cut 35/28 * 8 = 10 TPI. In position A4, the lead screw turns at 20/56 * 32/22 * 28/20 = 56/77 times spindle speed (or about 0.7273x). That would cut 77/56 * 8 = 11 TPI. At this point I had convinced myself the gearbox works and the threads per inch in the table are correct. What a marvelously clever piece of engineering! And all without computers and CAD. Jon

