Thursday, 26 April 2012

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.

Wednesday, 18 April 2012

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.

Wednesday, 11 April 2012

Wheel Building

It's surprising how little fettling you can do with the tops of four fingers missing (see below), however, I've tried to be a brave little soldier and this week I've built the wheels up. If you recall, I'd been itching to do this but I had to wait for the paint on the rims to cure properly. Lacing the rims to the hubs is easy and just requires poking spokes through the rim and screwing into the appropriate hole in the hub.

I started with the rear wheel as it is smaller and I can fit it into my wheel truing jig. 

Radially spoked wheels go from loose to very tight in about a turn and a half, so it is important to take it easy when starting off otherwise the rim may well be straight but not very round. The strength of the hollow steel rims means that there isn't a great deal that can be done about larger bumps and kinks in the rim, these have to be worked around as best you can. Also the wheel has to be trued so that the outer, hollow well where the tyring sits is true, not necessarily the sides or inner edge. 

Spoke grip in use.

The spoke key used is a special little clamp that is tightened onto each spoke in order to turn it. This takes a little time as you can imagine and means that the process cannot be hurried. These spoke grips are not uncommon and can be found relatively easily. They were made in quite a few variations and it is fun to collect as many types as you can. Not many people outside of this antique cycle world would know what one is used for but since they are small they are thrown in a drawer and forgotten about. They seem to have been made in large numbers as I have seen them advertised for sale in catalogues as late as the 1910s, though not for their original purpose. I made a small run of replicas some years ago and I've been using them since in preference to my originals.

Abingdon King Dick Spoke Grip advertised in 1912. This is the same Abingdon Works Co. that made the Abingdon ball head on the geared facile. I suspect that spoke grips were made in vast numbers and these advertised here are New Old Stock rather than current production.

Before I can lace the front wheel I need to machine the bore of the sun gear, this is the main gear that mounts to the end of the live axle. When the wheel is built it would not be possible to offer the axle up to the lathe to check for a nice fit.

This really does have to be accurate as all the torque to drive the machine
 relies on this fit, sloppiness would soon cause excessive wear and failure. 

Checking the fit.

Actually, I got a bit carried away and made the entire blank rather than just the bore. I like turning and the time just seemed to disappear. The gear is made from 4140 as it will need to be hardened. I may carry on and finish it off before I do anything else, I don't like leaving things half finished.

The front wheel was laced first and then trued by installing into the forks and truing in situ. 

Now that both wheels are complete, it is possible to get an idea of the scale of the bike by comparing it to other contemporary designs. It really is tiny.

As compared to a contemporary bicycle...

...and as compared to a contemporary safety.

In other news, Le Race didn't go exactly as planned. I'd stayed the night in Christchurch so I could just ride around the corner to the start in the morning. I got a good position on the grid and I didn't need a pee as the race started so pretty good so far. The usual high speed sprint down Colombo street (on wet roads) was followed by the first climb up Dyers Pass. I felt great and was pretty close to the pointy end of things, I was climbing well and riding comfortably when I got a rear wheel puncture. Glass, it's always bloody glass in Christchurch and this was on a new Vittoria open Corsa, my all time favourite tyre. I changed the tube and blew it up with one of those new fangled carbon dioxide cylinders but by this time I'd lost minutes and hundreds of cyclists had gone past me. Starting off again in my haste, I left my glasses at the side of the road. About now I realised that a decent time was not going to happen so I decided to just enjoy the ride. As I was now towards the back of the race amongst the slower riders, I found I was having to overtake everybody to climb at my comfortable pace, this is not too easy with large bunches without crossing the centre line and I was held up in the early stages. My bunch going across the flats was only about 8 riders and with most people having a go at the front we were still pretty slow. Le Race only really starts when you begin the climb up to Hill Top,

I love this section of the race and made up a lot of time on this hilly bit. 

As we approached Akaroa, I was catching riders I'd been with at the start, then came the final descent into Akaroa. Long Bay Road has a bad reputation as a dangerous descent on a bike. True, it starts above 600m and less than 6km later is at sea level. True, it has a crappy surface. True, it has many sharp bends, some of which are off camber, some tighten up on you and some are covered in gravel. True, the exposed saddle often has a nasty cross wind to catch you out.

Now, where Long Bay Road rejoins the main Christchurch Akaroa Road, the race route turns hard left and goes down the Old Coach Road. This road is very steep and requires care, unfortunately I was descending like a complete twat and lost the front wheel on the first right hand bend. Remember those wet roads? The slide took ages and I had time to consider my impending doom before I comprehensibly grated myself down the coarse chip seal. The marshalls were alerted by following riders and I was in the back of an ambulance in just a few minutes. When doing these kinds of rides, I make a point of thanking the marshalls as I ride past, it's volunteers like these that make these events possible, just something to consider. Anyway, the marshalls and the St. John Ambulance guys were fantastic. Roughly an hour later, I gingerly rolled down the remainder of the hill and crossed the finish line under my own steam to sympathetic applause.


Later as Sue & Colleen from the Akaroa Health Centre stitched me up, I reflected on how lucky I had been not to break anything. Now 10 days later, I'm well on the mend although my right knee will be a long time healing as I sanded it right down to the bone. I haven't looked at the bike yet, I daren't. It's my favourite 'modern' bike, a 1996 Argos built for me from the first batch of Reynolds 853 with lovely clunky 8 speed Campagnolo Record components. I think it's mostly OK. My beautiful new disco slippers are ruined as is my helmet. The clock read 4:11 as I crossed the line, my bike computer said 3:13. I think without the incidents, I'd have done the ride somewhere between 3:00 and 3:10, not too bad for a old, fat retrogrouch on a 'vintage' bike. I'll have to do it again next year. If my lovely wife will allow it.