Dave Shield 1  08/01/2019 18:40:46 
5 forum posts  Can anyone please advise I am building a MJ ENG 2" scale Fowler compound road loco and I am having trouble cutting the gears for the diff. Started with the pinions,less to mess up,and finished up with large gaps and very thin teeth.Tried both parallel and tapered depth. DP 8, cutter No.8, 11 teeth. I have read Ivan Law's book and various items on the tinter web,and suspect that it needs a No. 7 or 6 cutter. The calculations call for a No.8 cutter. Had no problems with the spur gears.
Cheers Dave in Cornwall.

Neil Wyatt  08/01/2019 19:06:05 
Moderator 15700 forum posts 659 photos 73 articles  There's an uncorrected error in the book, you have to use cosine not sine in the first two calculations, which can lead to errors. Has this caught you out? Otherwise the method is reliable. Neil 
JasonB  08/01/2019 19:19:35 
Moderator 15034 forum posts 1532 photos  how did you calculate the cutter to get a No8? I make it 1/sin 18 deg 25min x 11T = 34.7 or 35T which is a No4 Could be wrong, I went with the cast gears, best photo I have of the shape Edited By JasonB on 08/01/2019 19:24:03 
Andrew Johnston  08/01/2019 19:33:14 
4497 forum posts 520 photos  To calculate the cutter number one uses Tregolds approximation. I won't go into the maths but essentially it uses the cone angles of the mating bevel gears to come up with an equivalent number of teeth which then determines the cutter number. For a bevel pinion and gear with intersecting axes at 90 degrees the cone cone angles of the two gears will depend upon the number of teeth on each gear. If there are n teeth on the pinion and N teeth on the gear, and the pitch cone angles are a and A respectively then: tan(a) = n/N and tan(A) = N/n How you use this to calculate the equivalent number of teeth will depend upon the method used to machine the bevel gears, ie, tapered depth teeth or parallel depth teeth. I'm not familiar with the details of the specific engine, so to go further we need to know the number of teeth on each gear and the method to be used for machining. Andrew 
Neil Wyatt  08/01/2019 19:36:35 
Moderator 15700 forum posts 659 photos 73 articles  Can we share details of the gear measurements? Neil 
JasonB  08/01/2019 19:41:19 
Moderator 15034 forum posts 1532 photos  Should have the details here, click for larger image Andrew's formula gives the 18 deg 25min that I used earlier and that is given in the table. Edited By JasonB on 08/01/2019 19:44:37 
Neil Wyatt  08/01/2019 20:43:33 
Moderator 15700 forum posts 659 photos 73 articles  Ivan Law's formula concurs, it gives 34.6 for No.4 cutter. Neil 
JasonB  08/01/2019 20:55:44 
Moderator 15034 forum posts 1532 photos  It does seem big though as there is not that much diameter difference from the inside and outside diameters of the pinion maybe that should be Cos too? 
Neil Wyatt  08/01/2019 21:43:53 
Moderator 15700 forum posts 659 photos 73 articles  Posted by JasonB on 08/01/2019 20:55:44:
It does seem big though as there is not that much diameter difference from the inside and outside diameters of the pinion maybe that should be Cos too? I did wonder... when angle is 0 the pinion would be a 'normal gear' and 1/(cos 0) = 1 When angle is 90 degrees the pinion is infinite diameter = rack and 1/(cos 0) = 1/0 So I think yes it should be Cos too. Edited By Neil Wyatt on 08/01/2019 21:48:02 
Neil Wyatt  08/01/2019 21:49:44 
Moderator 15700 forum posts 659 photos 73 articles  That would give 12 teeth for cutter number 8... Hmm. Neil 
Andrew Johnston  08/01/2019 22:38:18 
4497 forum posts 520 photos  There seems to be some confusion here! The drawing posted by JasonB clearly shows bevel gears with a tapered profile and the pitch diameters specified at the outer edge. So these are desgined as proper bevel gears, not parallel depth bevel gears. The values given on the drawing for the pitch diameters are correct. The pitch cone angles are incorrect; they should be 18° 26' and 71° 34'. For the ODs I get 1.612 and 4.206"; very close to drawing. I haven't checked the other values. For proper bevel gears with the DP specified at the outer edge the equivalent number of teeth used to select the cutter is the actual number of teeth divided by the cosine of the pitch cone angle. The equivalent values are 11.595 and 104.355 for the pinion and gear respectively. So a #8 cutter for the pinion and #2 for the gear. This agrees with the results I used in the design and manufacture of the bevel gears in my traction engine differential, and they mesh very well as shown with these prototype gears in aluminium: The calculations in the Ivan Law book are for parallel depth bevel gears. These are not the same as proper bevel gears and the same calculations for cutters do not apply. Parallel depth bevel gears are designed using a given DP at the inner edge of the tooth, not the outer edge. For parallel depth bevel gears the formula for calculating the equivalent number of teeth is 2 times x times the diametral pitch, where x is half the pitch circle diameter at the inner edge of the teeth divided by the sin of the face angle. For a parallel depth bevel gear the face angle is the same as the pitch cone angle. Andrew Edited By Andrew Johnston on 08/01/2019 22:40:41 
JasonB  09/01/2019 07:51:12 
Moderator 15034 forum posts 1532 photos  Thanks for the insight Andrew. Doing a few quick sums The OD of the inner face of the pinion works out at 1.296" which for 11teeth would work out at 10.03DP and that would go some way to explaining why Dave is getting large gaps and narrow teeth. If we then work with the 10.03DP to get how many teeth would fit around the outside OD that gives 16.13 say 17T so a No6 cutter. This does not agree with law's method of calculation as you get either 12T or 35T depending whether you use Sin or Cos Dave, worth working it out in more detail before buying cutters and making swarf as things will need adjusting if using off the shelf 10DP cutters.
Edited By JasonB on 09/01/2019 07:59:18 Edited By JasonB on 09/01/2019 08:18:27 
JasonB  09/01/2019 08:27:00 
Moderator 15034 forum posts 1532 photos  Interestingly working out the cutter size using Andrews formula with 10DP comes out a 35.8T, close to using Cos from law's book. ( 2 x 0.648 x 10 ) / 0.362 = 35.8 Edited By JasonB on 09/01/2019 08:29:15 
Andrew Johnston  09/01/2019 10:08:06 
4497 forum posts 520 photos  Dave needs to tell us which method he is planning to use to cut the gears. Simply doing the calculations for the parallel depth method and applying them to a design intended for proper bevel gears will not result in a differential that will fit without changes to the rest of the engine. It's a significant amount of design work to change a mating gear set from proper bevel to parallel depth. Not simply a case of changing the machining method. When I started redesigning the governor for my traction engines I initially decided to use the parallel depth method for the bevel gears. But using an integer value for the DP at the inner edge of the gears created so many difficulties fitting the gears into the existing casting that I reverted to making proper bevel gears: Andrew 
Andrew Johnston  09/01/2019 15:19:09 
4497 forum posts 520 photos  One more thought; if one is cutting a 'proper' bevel gear with tapered teeth on a milling machine then an ordinary involute cutter is not acceptable. If one is using a standard involute cutter the small end gap will be wider than it should be. The method requires a cutter that has the correct curvature for the outer edges of the teeth, but will go through the gap at the narrow edge. To achieve this special, narrower than standard, involute cutters were available, stamped BEVEL. I don't think they're available now. I have used one, but a long time ago when I had the resources of the RAE Farnborough main workshop to hand. Andrew 
Norman Rogers  09/01/2019 16:26:02 
13 forum posts  Hi, Andrew: you may remember you and I had some similar correspondance a while back .... I managed to find a company that could manufacture these special BEVEL cutters and ordered those required for my D&NY TE (12DP). Haven't cut the bevel gears yet but at least in theory I now can. The firm in question is C R Tools in Sheffield (usual disclaimer). Hope this helps Norman 
Neil Wyatt  09/01/2019 16:39:09 
Moderator 15700 forum posts 659 photos 73 articles  I'm slightly more, not less confused. Isn't 2 times half the PCD the same as the PCD? Also surely it's divided by cosine face angle whether working at the inner or outer end of the teeth? The difference just being that you use a cutter equivalent to a full tooth space at one or other end of tooth. Ivan uses sin back cone which is = cos face angle as they are complementary for parallel gears. His choice of 45 degrees for the example is unfortunate as not only does it mean face angle = back cone angle, but sin 45 = cos 45 = 0.707. N. 
Dave Shield 1  09/01/2019 18:31:13 
5 forum posts  Thank you for replying to my problem. I used cos. in the calculations and came out with 11.595 for the teeth on the pinion. I did expect problems as it is a small pinion with relative large teeth and outside the range of a No. 8 cutter. However there was pictures on MJ's site showing what the pinions look like when finished. Inspection of the pictures seemed to indicate a smaller No. cutter. I think my problem is that I tried to combine cutting a true bevel gear with a parallel depth one. For the cost of a bevel gear cutter to be used twice, the gears cut by MJ Eng would be well worth it, but not so much fun. I have worked on the dark side all my life, electronics, instrumentation, and electrics, good to work on problems you can see. Cheers Dave

Andrew Johnston  09/01/2019 19:55:49 
4497 forum posts 520 photos  Thanks for ther reminder Norman. Out of idle curiosity are you prepared to give an indication of the cutter cost? Andrew 
Andrew Johnston  09/01/2019 20:20:07 
4497 forum posts 520 photos  Posted by Neil Wyatt on 09/01/2019 16:39:09:
I'm slightly more, not less confused. Let's see if we can cure that. First, yes the divide by two and multiply by 2 is superfluous, but I thought I'd better quote direct from the source rather than be a smartypants and get it wrong by a factor of 2. The formula for the equivalent number of teeth for a proper bevel gear uses the pitch cone angle, not the face angle. For gears with axes at 90°, given that sin(x) = cos(pi/2x), the two methods are equivalent. We can do a thought experiment to see if sine or cosine is correct for the parallel depth case. Let's assume that sine is correct. Let the face angle increase; when it reaches 90° then the value of sine will be 1. In which case the formula simply gives the number of teeth on the gear, pitch circle times the diametral pitch. But what's a parallel depth bevel gear with a face angle of 90°? A spur gear! Conversely if we let the face angle decrease to zero then the value of sine also goes to zero. In which case the equivalent number of teeth becomes infinite. But a parallel depth bevel gear with a face angle of zero is a contrate gear; essentially a rack bent into a circle. Andrew 
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