Member postings for Andrew Johnston

Well if you will persist with all this tiddly stuff what do you expect? Incidentally I make 18³ equal to 5832.

I build big stuff as an antidote to work electronics. The current job is going to require using ICs that are 0.8mm square with 4 solder balls underneath on a 0.4mm pitch. For space reasons we will need to use 0201 passives; that's 20 thou by 10 thou. I can't even see the darn things without a magnifier.

Andrew

Ooopsie, I should have multiplied the face width by the sine of the cone angle before subtracting from the outer PCD. Doing that I get a DP  value of 7.874 for the inner ID. Closer to John's value but not identical for some reason?

The 10 tooth pinions in my differential are undercut:

But that's just a consequence of the way I designed them. If I was doing it again I'd try and tweak the gear tooth parameters to eliminate the need for undercut.

Andrew

Edited By Andrew Johnston on 23/10/2020 11:58:59

Mass scales as a cube law. So on my 4" scale engine I'm down by a factor of 27 on mass. It's the main reason why scale governors that rely on mass for sensing are difficult to get working. I've done my best to ameliorate the problem by making the balls slightly oversize and making them from tungsten alloy. Even the screw holding the ball halves together is made from a tungsten TIG electrode. Platinum was ruled out on cost grounds.

Andrew

The astute reader may have noticed that I've been posting again today. Like it or lump it I intend to continue.

Regarding the tasks mentioned above I now have the wheels for my traction engine complete with rubber tyres:

I'm very pleased with the rubber tyres, less so with the rust from the vulcanisation process. I've got rid of a lot of it with wire wheels and a drill. But I've also bought a cheap blast gun and some garnet grit to get rid of the rest.

The safety valve design is on hold.

I now understand the basics of spiral bevel gears and also the difference between involute and octoid tooth forms. So it's now a case of modelling something I can 3D print and then machine.

A further distraction has occurred. Following discussions on the MEM forum I have found some old notes on the internet on the design of skew bevel gears. Of course I am aware of the work by Kozo. But I think his designs are based on hypoid gearing and the tooth profiles are significantly asymmetric. If one looks are drawings, and photographs, of the logging locomotives that used skew bevel gears the tooth forms are symmetric and look like straight tooth bevel gears. The design notes I have found use symmetric tooth profiles as per the full size engines. So I plan to model same in CAD and 3D print them to see if they work.

Talking of work I am now working for the first time in ten months and have been dragged into the 21st century with Zoom meetings for the first time this week. Work has to take priority as the savings are depleted. And we have a reputation with the client for delivering late so we absolutely have to deliver what we say, when we say this time. I am now delving into electrochemical gas sensors, potentiostats and transimpedance amplfiers, although given the large effective series capacitance in the sensor the output amplifier is more like a differentiator, complete with all its noise problems.

Andrew

Starting with 44 teeth and 6DP for the design as published we get a PCD at the outer edge of the bevel gear of 7.333". The face width is given as 57/64". If we subtract twice that from the outer PCD we will get the inner PCD, ie, 5.552". If we divide 44 by the inner PCD we get the DP at the inner face. I make it 7.925. That's close enough to 8 to wonder if it might be worth tweaking the face width to make it exactly 8. The PCD for a 44 tooth 8 DP bevel gear is 5.5". Subtracting that from the PCD at the outer edge and dividing by two will give the new face width. I make the answer 0.9167" or just under 59/64".

So if you increase the face width to 0.9167" then you should be able to cut the gears with an 8DP cutter, using the correct number of cutter according to Tregold's approximation. How to calculate the cutter number is in the book, but not described as Tregold's approximation, nor why it is an approximation.

Caveat: I'm making this up as I go, and I've just started my second beer. I expect Jason will be along to correct me if I've got it wrong.

Andrew

I wondered if that might be the case when I was composing my reply. May be it also depends upon the number of teeth on the pinion? I recall a post on here, or TT, where the poster had made a bevel gear with a tooth count that was not divisible by three so that his differential would not fit together. He got around the problem by spacing the three pinions at unequal angles around the circumference.

Andrew

Hunting can occur as a result of the governor being too sensitive, but it can also be the result of unwanted friction in the valve operating mechanism effectively creating a deadband.

Andrew

Depends on the rivet size and material?

Andrew

Well you could, but I've never heard of it being done and I can't immediately see why one would want to. Enginemen of old would have been interested in getting the job done, taking the money and moving on. Not faffing about changing pulleys and belts. I doubt they would have had any accurate way of measuring engine speed anyway.

Andrew

It won't. As I mentioned straight tooth bevel gears are designed using the DP at the outer face while parallel depth bevel gears are designed using the DP at the inner edge. So if you design a 6DP parallel tooth bevel gear with 44 teeth the pitch circle diameter (PCD) will be correct at the inner edge. But at the outer edge the DP will be smaller than 6 (depending upon the face width) and the PCD will be correspondingly larger.

Take the following with a pinch of salt. While I've designed and made a fair number of bevel gears I've never needed to use the parallel depth method. You need to set the outer DP to 6 and then work out what the DP will be at the inner edge. Presumably in proportion to the face width and cone distance. Once you have a value for the inner DP (almost certainly not an integer value) you can then design the gears as per the book. Since the inner face DP will not be standard you will need to make your own cutter. I don't know if the parallel bevel gears so designed will have the same back face to back face dimensions as the original gears. The values should be close, but I don't know if they will be identical.

On MEM Don Darbonne (Don1966 I think) has published an Excel spreadsheet for automating gear calculations including parallel depth bevel gears.

Andrew

Dream on!

The centrifugal type governors, with a fixed relationship between ball position and valve opening, are not intended to work with varying control speeds. They simply attempt to control a single speed (set during design) as the load varies. It is inevitable that a change in load causes a change of speed. The objective is to minimise the change of speed with change of load. In terms of the s-plane that means the poles need to be as close to the imaginary (y) axis as possible while still remaining in the left hand side of the plane.

Pickering governors (as on my traction engine) have a "speed" adjuster worm and worm wheel. But this is a misnomer. An early Pickering patent makes it clear that this control is not intended to adjust the governed speed. Later Pickering patents came up with varying ways to adjust the governed speed by changing the relationship between ball position and valve position while not affecting the operation of the governor.

In summary centrifugal governors are some way short of being ideal. Where speed control is vital, as on mill engines, governors were developed that controlled the valve events (varying cutoff) rather than a simple throttle valve.

I'm not convinced that simple governors are feedback systems. I think they're open loop and simply move along a speed/load line as the load varies. There is no attempt to correct for the speed error that arises from any change of load.

Recently there was an intense debate on TractionTalk concerning governors. It was stated that governors work in the z-plane, ie, sampled data transforms rather than Laplace transforms. Given that the proponent of the idea got confused about sampling frequencies and Nyquist rates I wasn't convinced! However, I would agree that the stability of the system relies to some extent on the response of the whole engine, not just on the governor and valve.

Andrew

If we place one pinion at the top of the bevel gear then the teeth on the pinion will be in a set, but arbitrary, position. If we now place the second pinion 180° apart then the orientation of the teeth on the second pinion will depend upon the number of teeth on the bevel gear. If the number of teeth on the bevel gear is divisible by two then the orientation of the pinion will be the same top and bottom and the second bevel gear will fit as the teeth on the pinions will be oriented the same top and bottom. However if the number of teeth is not divisible by two then the orientation of the bottom pinion will be different. So the alignment of the pinion teeth will be different between top and bottom pinions and the mating bevel gear will not fit.

Andrew

Edited By Andrew Johnston on 22/10/2020 14:36:21

The mathematics behind centrifugal governors is well established and was first studied by Maxwell in 1868, presumably as a bit of light relief after sorting out electromagnetic theory. Essentially the governor is controlled by a second order differential equation, the solution of which are two co-incident real poles, or more likely a pair of complex conjugate poles. An understanding of poles on the complex s-plane helps to understand the behaviour of simple governors.

See this thread for a ramble through the operation of governors and my thoughts on trying to make a working scale governor:

**LINK**

Andrew

Certainly, although I don't know if it was ever used full size. Some late Aveling and Porter road rollers used an arrangement of spur gears and pinions to achieve a differential function without the need for bevel gears.

Andrew

How many pinions in the design? Assuming that the pinions are evenly spaced then the number of teeth on the gear needs to be divisible by the number of pinions. So 37 teeth must be wrong as 37 is a prime number. If 44 is correct that implies 2 pinions as 44 is not divisible by 3.

Were the gears orginally designed using the parallel depth method? If not then your calculations are meaningless. Normal straight tooth bevel gears, with tapered teeth, are designed using the DP at the outer face. However, parallel depth bevel gears are designed using the DP at the inner face, so a standard involute cutter can be used.

It's difficult, if not impossible, to re-design normal bevel gears to be parallel depth while keeping the outer PCDs the same and also making the DP at the inner face an integer.

When I was looking at the bevel gears for my traction engine governors I started to re-design using the parallel depth method. But keeping to standard integer values of DP at the inner face simply didn't work. If I was going to design and CNC machine the gears anyway then there was no point in using the parallel depth method. So I stayed with normal straight tooth bevel gears:

Andrew

Paul is correct; the neutral axis is not usually at the midpoint of the material, but is closer to the inside of the bend. I normally do sheet metal design using the sheetmetal function in Alibre CAD where the K-factor is 0.33 by default, ie, the neutral axis is one third of the material thickness from the inside of the bend. Assuming that a box and pan folder is being used the other important factor is the bend line, ie, the start of the bend. This is where the material is clamped. Based on previous work if I made the part shown I'd expect overall dimensions to be within 0.1 to 0.2mm.

For large bend radii, as in this wheel rim, assuming that the neutral axis is at half material thickness is valid:

The length of material needed to get the final wheel diameter was based on the diameter at half material thickness. After rolling and welding the final wheel diameter was about 15 thou off the target of 14.5".

Andrew

If I recall correctly I expressed an interest in buying the larger cutters, but AJAX never bothered to respond.

Andrew

Thanks for the encouraging replies. I've also had some PMs and a couple of 'phone calls, in one of which I was smacked round the head and told to stop being an idiot.

The plan is now to take a break and concentrate on the paid for work that is finally coming in. After that, like it or lump it, I'll be back. I will still be reading, and responding to, PMs. The timing may be slow though, as for reasons never explained I no longer get an email to say I have a PM waiting.

I'm not entirely abandoning the traction engines and other engineering. There are three main tasks upcoming:

1. Collect the set of wheels from the rubber tyre company and get the second engine on it's wheels.

2. Re-design the safety valves to be pop types.

3. Understand the maths and see if I can create a 3D CAD model of a spiral bevel gear. If I can model it then I will be able to 3D print and/or machine it.

Andrew

Following an unfortunate post in a recent electronics thread that was misconstrued I got excoriated. That has been the trigger, if not the root cause, of me deciding to take leave from the forum.

One thing the current panic has done is make people re-assess what they're doing and it's worth. I'm spending way too much time on forums and not enough time actually doing things.

On a more practical note after nine months of enforced idleness I've now got some work flowing in. So that takes absolute priority.

I understand that deleting my albums would remove the pictures from posts. So, for the time being, the albums will stay.

Andrew

There are two basic products. Engineers blue in a tin is a sticky paste used to identify high points when scraping. For instance if one wants to scrape a surface flat against a reference (surface plate) the work is smeared with a thin layer of engineers blue. The work is then pushed across the reference surface. The points where the blue has been rubbed away are high points and need to be scraped. Then repeat as required. The watery blue liquid in a bottle is for marking out. It's painted or wiped on where it dries and leaves a thin blue sheen. Scribed line then show up more clearly.

Andrew