Tyres, Teeth & Tuhoe

I've haven't had much time to actually do much this week although I have spent time working out how to make the backbone, more on this later.

The tyres are red, they are not pink darling.

I've had the tyres fitted to my wheels, or more accurately, the tires since I've used the American system rather than the English one. The English system uses a spiral of wire moulded within the rubber. The tyre is cut too short for the rim and and inch or so of the spiral exposed on either end of the length. Then by twisting the rubber the wrong way for the same number of revolutions as coils are exposed on the spiral, the tyre can be joined and the spiral screws into itself and the gap is closed. The loop is then stretched over the rim and is held in place by tension only. This is usually OK for normal use but recent batches from the UK have been a bit crap. This is what can happen when crap rubber is used, the Rider is Jack Castor from California, he was quite seriously injured but is now fully recovered. This happened on an NZ tour a few years ago, Jack was descending from the Otematata saddle between Omarama and Kurow, notice the 'loop' forming in front of the wheel before it all goes pear shaped.

In contrast the American system uses a rubber extrusion with an empty hole through the middle, the rubber is cut too long for the rim and wire fed through the hole. The wire is tensioned on a special machine in such a way that the excess rubber gets bunched up evenly around the wheel whilst leaving a short section of each end exposed. The two ends are trimmed and silver soldered together. When the jig is removed the gap closes up tightly. The rubber used has been sourced directly from the states and is of very high quality, it wears well on our rough roads but is still grippy enough to be safe in the wet.

I painted a couple of pinstripes on the rims before the rubber was mounted. I've been collecting images of original Victorian pinstripes for years now. Every time an original machine gets restored another unique reference point gets lost. But don't get me started on that. It is surprising how gaudy some of the Victorian machines were. We tend to think of the Victorians as very straight laced with stiff upper lips and little skirts around table legs lest the men think unseemly thoughts etc.. Actually, I'm not sure that the table legs thing is true but it's a good story. The point remains though, that to our modern eyes, some of the pinstriping and painted decoration seems way over the top. The double pinstripe on each rim is common, I've seen it on many original machines.

Tax free teeth?

Also this week, I've got the gears back from the gear cutter, he has done a fantastic job and I'm very pleased with the result. I will not say if he waived the GST when I waved cash, that would be rude. They need to be lapped to polish the faces but there is also a lot of machining to be done on both gears anyway. I'll oil these and set them aside for the time being as I focus on the rest of the frame so I can get the bike sitting on it's wheels.

This week I'm going to make some more rollers for my elliptical tube rolling mill, I need to make two sets. One for the elliptical backbone and one for the rear forks. The facile I am copying is a later model and has fully tubular fork blades either side rather than the half open style of earlier machines.

In other news, the family was at a loose end on Saturday so we took a trip on the MV Tuhoe moored at Kaiapoi.

MV Tuhoe.

It was fantastic in that old fashioned, slightly naff way. Sunday's trip coincided with the 'Super Moon' so the tidal river was very high.

Oh, that's super.

I particularly liked the way we were allowed free access to the engine room. If you find yourself at a loose end, I can highly recommend it, just wrap up well if an Easterly is blowing.

The engine room complete with engineer complete with engineer's cap.

Gear Blanks

After all that geary theory, it's time to get our hands dirty again. This week I've been making the gear blanks. I had previously started the sun gear blank because I needed to machine the main bore before I built the wheel up, All that remains is to machine the special key way that locks the gear to the front hub.

These pictures illustrates the key way, 

a tapered key fits into the shaped key way and is 

drawn up the matching taper on the hub by a locking screw. 

The original that I measured came apart very easily and has obviously been apart before as the tapered key and screw have both suffered at the hands of an enthusiastic hammer owner. The key (pardon the pun) to getting this kind of interface to work successfully is to have very close tolerances and as it turns out I had two attempts at the tapered key before I was happy. I may need to make another after everything has been hardened and plated, the tolerances are that tight.

The first job is to drill a hole that just grazes the edge of the bore 

and then countersink the outer end for the locking screw to locate in. 

I actually used two end mills for this job rather than a drill.

The next job is to flip the sun gear over and mill the back of the gear 

from the hole into the bore to create the key way. 

Note that the plug to bolt the gear to the vertical slide already 

had a recess machined out. This cut has to be at exactly the right depth.

Then we can machine the key itself, first job is to drill and tap

 a 1BA hole up the centre of a length of barstock. 

The original really was 1BA, I measured it very carefully.

Then without removing the work from the chuck, remount the chuck 

on the dividing head and mill away the excess to form the correct shape.

Finally, mill the 4 degree taper, this is where the size become super critical. 

With such a short taper, if the key is too tall you can't assemble it 

and if it is too short the key bottoms out as it is tightened.

Next make the locking screw, this is just simple turning and threading with two slots milled at opposite edges to adjust it. Of course, I also needed to make the special tool to do the adjusting...

Finally we can test the assembly of the lock.

Then I just need to make the blank for the planet gear, which is also just straightforward turning at this stage. All the fiddly stuff comes later.

Gear blanks ready for the teeth to be cut.

In other news, last weekend we had a local steam extravaganza at Steam Scene. I took the kids and we had an excellent time. A particular favourite being the miniature train rides which seemed to go almost to Christchurch and back. I was examining the gearing (for topical reasons, you understand) on a traction engine when the owner appeared and asked if I was "Claudia's Dad". It transpired that our respective daughter's were friends. During the course of our conversation, the geared facile came up. I enquired where she got her casting done locally and was referred to a small, local Christchurch foundry that should be able to help. I took my patterns and a photo of a geared facile around on Monday lunchtime. Well, again, it turns out we have mutual friends and had attended many of the same events together, we just hadn't met yet. The upshot is that my parts will be cast in steel and will be ready next Friday. I'll be sure to let you know how they turn out.

In more other news, On Sunday afternoon I helped an excitable, young Tinkerbell build her faux pathracer in my workshop. She arrived laden with Jaffa Cakes (I don't do this for free you know) and we proceeded to prep the frame before using vast quantities of my spare parts. Two of her chums from the local tweed riding scene, Dylan and Pete, also arrived and helped out. We finished it off, sans brakes, and she was able to ride it up and down the street before heading home very happy. She has since added some brakes. Tweed Pete also gave me a recommendation for a local gear cutter. I'll give him a ring tomorrow.

A lecture on gears

Pay attention at the back, there'll be an exam later. I'm looking at you Middleton.

I've needed to learn a little about gears and gearing theory in order to reproduce the geared facile. This has all been a lot of fun (we may have to disagree on this point, I'm a mathematician and my idea of fun may differ slightly from the norm) and I need to share my findings. I'm not going to go into great details but a Google search will yield many results on this stuff if you are interested.

Cycloidal or Involute?

The first thing to determine is the type of gear profile, there are two contenders: cycloidal or involute. Historically, cycloidal gears were used almost exclusively up until the late 19th century when the new fangled involute profile quickly became the standard. Cycloidal gears are still traditionally used in clock making and have a devoted following. Involute gears have certain benefits, such as a tolerance to incorrect gear spacing, that makes them attractive to industry. It is easy to distinguish between these profiles by eye.

I've been unable to find an absolute date for when the involute profile was introduced, all references I've seen suggest the end of the 19th century. Of course this is the exact time frame when the geared facile was being produced.

Examination of the original gears clearly suggests that they are involute, 

which means that Ellis & Co. were at the cutting edge of the current technology in 1887.

So now that we have established that the gears are involute, we need to calculate the size of the teeth. For gears in a gear train to mesh accurately they need to have some commonality in the tooth size, this is known as the Diametrical Pitch (Pd), which is the ratio of the number of teeth to the pitch diameter. All involute gears with the same Pd will mesh accurately.

All original faciles that I have measured have 37 teeth on the sun gear and 18 on the planet gear. I stand to be corrected on this but the literature of the day backs this up. The final gear ratio in this simple epicyclic train is calculated as follows:

gear ratio = wheel size in inches x (driver + driven)/driven

with a 40" wheel, 37 tooth driven sun gear and 18 tooth driving planet gear we get a gear ratio of 59.46" or the equivalent of a penny farthing with a 59.46" wheel. Ellis and Co. offered the geared facile in three sizes 36", 38" & 40" and claimed gear ratios of 54", 56" & 60" resp. The actual calculated values are 53.51", 56.48" & 59.46" resp, it seems that Ellis & Co. liked to keep things even at the expense of accuracy.

Note that it is very important that at least one of the gears has a prime number of teeth, this ensures that the gears will wear absolutely evenly. With a pulsed power delivery such as a bicycle, if this were not the case, spots of high wear would rapidly occur where the same tooth was repeatedly under peak load.

So how do we calculate the Pd to be used? We have the number of teeth and we also have the centre to centre distance for the gears, from the literature and also from my own measurements I know that the gears ran on a 3" crank.

Centre distance = ((driver teeth + driven teeth)/2)/Pd

gives us a Pd of 9.16666 teeth per inch

which is unfortunate since commercial gear cutters are always sold as whole numbers (and the odd half size). If I use a Pd of 9, I get a centre to centre distance of 3.056", a little too far off for comfort. Fortunately gear cutters in metric countries use an alternative to Pd known as the module.

Module = 25.4/Pd

so we need a module of 25.4/9.1666 = 2.77

metric gear cutters are available in fractional sizes, the closest to 2.77 being 2.75. If I use a module of 2.75 my centres work out to 2.977", less than half the error of using Pd 9 cutters, also remember that tolerance to incorrect spacing that involute gears have?

The last thing to calculate is the outside diameter of the gear blanks, this is given by the following formula:

OD = (teeth + 2)/Pd

this gives sizes of 4.222" for the sun gear and 2.165" for the planet, which match closely to my measurements of the originals.

gear cutters are available in sets of 8, with a different cutter used for a range of teeth

#8 12-13 teeth
#7 14-16
#6 17-20
#5 21-25
#4 26-34
#3 35-54
#2 55-134
#1 135-rack

So I need to buy cutters #3 & #6 for mod 2.75. The only other variable to consider being the pressure angle which I won't go into. As it happens it was cheaper to buy a full set rather than individually.

I had originally intended to cut the teeth myself but now that I have the cutters in my hand, I've realised that my machinery simply isn't massive enough for the job, these are big teeth. Teeth are usually cut at one pass and require an immensely stiff setup to cut the bigger sizes. I'll contact a local gear cutter when I finish the blanks off. I'd rather get a good job done than screw things up.

Has anybody managed to get here yet without falling asleep?

In other news, I've been for a gentle 50km ride at the weekend. My first since the Le Race debacle. The only bits that still hurt are two fingers on my left hand and my right knee. My right knee was OK after the ride, not great but OK. I still haven't looked at the crashed bike yet. For the ride I selected a late 1940's Raleigh Record Ace (RRA), this was for several reasons: it's very comfortable and I still have a pair of shoes for the toe clips that aren't munted from a recent crash.

A late 1940s RRA. Red, of course.

Not disco slippers.

In more other news, Mr. Middleton and partial family have been for a visit. I was unable to provide an earthquake which was a source of some disappointment. However Mr. Middleton was able to console himself by stealing some of my 4130 seamless tubing. I think he is going to use it to make something from this book written by somebody or other.

Also, Tinkerbell wants to come and see my magic cupboard. Actually, she wants help building up a faux pathracer and I happen to have lots of bits that she needs. Sadly, she intends to paint it british racing green!

Seriously though, there is only one colour suitable for bicycles and that's red[1]. We all know that.

[1] Unless it's black.

Oh, and I lied about the exam.