Step 5
I have positioned the wheels, left to right, so that I can hang weights on them, as I previously did, and have the wheels turn the correct way around.There seems to be no information on the web about how different amounts of friction are present and influence the clock's workings.
Lets start with the basic facts of the three arbors - I shall ignore the pinion addition to the Inertia of the wheels, but the weights will include them as well as the connecting rods.
What
Crown 3rd Wheel Minute Wheel Drum Combined weight gms 88 143 525 107 Radius of wheel cms 5 7.5 12.5 1.5 Inertia (1/2 x M x R x R) 1100 4022 41016 120 Revolutions 60 10 1 1 Now I have no idea what I'm doing (what's new!), but the Moment of Inertia of the wheels will be constant during this phase (until I cut out the middles), but we have 2 sources of friction - Arbor and Teeth. What I want to know is the proportional amounts of these two frictions and how, by sanding/shaping/polishing, they can be reduced.
There are a couple of points I have noticed straight off (but I do not think leaving the arbors at 30cm length helps -.
- The Minute wheel brass arbor bends downwards a touch when a 3lb weight is attached to the drum and I do not think this is caused by movement of the support (but maybe).
- There is a slight vibration on the 3rd wheel arbor, and hardly on the Crown, when the Minute wheel revolves at a fast speed. This could be due to my finger force moving the Minute wheel sideways, or more likely bad teeth
The Minute wheel was not balanced and I had to add 3gms at 9.5cm radius at tooth 58. This was strange as the join in the wood runs through teeth 6 & 36 and the backside leaves a groove. This almost implies that the wood filler (filling the groove) is denser than the MDF! After balancing the vibration on the 3rd arbor disappeared.
The starting position was that 7gms gave a 396º revolution of the Minute wheel, which reduced to 326º when the Drum was engaged. [I weighed washers to use as weights and worked out their individual weights - small ones were 0.877gms and the big ones 4.9gms each.]
The 3rd Wheel required 2.6gms to give a 360º revolution.
IF my logic is correct and there is no friction in the teeth (ah ah!), then it would require roughly 33 gms (i.e. 10x2.6 + 7) when the two wheels were engaged to give around a 360º revolution. The actual figure was 57.8 gms. I think this implies that there is 25gms x 12.5cm worth of friction (increase of 175%). However to get a half revolution it only required 20.2gms compared to a calculated 14gms (as it only needed less than 1 gm to produce a half revolution of the free standing minute wheel) - only a 144% increase.
Why does it require a weight of 7gms to do a revolution of the Minute wheel, but only 1 gm for half a revolution? Well I think it is to do with the speed of the wheel and the more force needed to accelerate the wheel, as Kinetic Energy = 1/2 x M x velocity^2. IF that is correct, then it goes someway to explain the extra force needed to revolve the 3rd wheel quickly. Perhaps I really need to time the speed of the revolution - but that would not be very accurate, although it takes around the same time 4.8 > 4.5 secs for a full to half revolution. The weight drops off after a quarter turn and the rest is the friction slowing down the momentum of the wheel. I'm not sure this is the most accurate way, especially as the speed is so fast compared with the final running speed of the clock.
Well I reckon that is not the way to test the wheels, but I can come back and compare this when I've finished sanding the teeth.
Why didn't somebody say? - the obvious(?) way to test, is to use the drum and weight to slowly revolve the wheels and see where they bind or slow down. This is so much more accurate than doing it by hand or eye (which seems to be the way suggested on the web!).
So I hung a small water bottle (very easy to top up or reduce) from the drum and started with all the pinions engaged. 500gms were needed to revolve them all, with a little binding on a few teeth. But this is not the way to do it, as I should start with the just the Minute and 3rd wheel and get them to revolve perfectly (some hope!) before adding the extra variable of the Crown wheel.
I started with a weight of 216gms, for the two arbors, and after 4 bashes of sanding various Minute teeth, I got it down to 169gms. It is also very handy having the teeth numbered as one just records which are binding or slowing the wheel down.
I tried sanding the teeth with 600 grade, but it did not make much difference. However polishing the 3rd arbor was a great improvement. The 3rd wheel only then required 1.7gms (down from 2.6gms) to give a revolution. It also resulted in the both wheels revolving in 60% of the time, compared to a non-polished 3rd arbor, for the same 169gms weight!
I then made (another) mistake polishing the Minute arbor. I used too much pressure and scored it - so no gain there! Guess I will buy a stainless steel rod, which should not flex so much.
Interesting that moving the arbors in and out did not really make much difference to the weight required to revolve the wheels.
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