Mark Kelly said:
The Hertz formula will only give you the amount of elastic deformation, and hardness is a plastic property. Even if you have the maximal stress, you'll need to relate it to the yield strength (which is alloy dependent in steels).
I'd have to sit down and give it some thought, but I'd be concerned with cyclic fatigue of the ball more than any other component.
The information I have is that the major mechanism of failure is shear stress in the deformed material under the contact point. You are of course correct that the maximal allowable shear stress is related to the yield stress and these are dependent on alloying and hardening.
Failure of the ball seems relatively uncommon, I *think* it's only going to be a problem if the thrust plate material is as hard as the ball material. I was going to proceed on the assumption that the thrust plate would be softer than the ball (or ball end), thus the hardness of the ball isn't too important..
The calculator seems to give real world results - I know someone who design a table with a sapphire ball riding on a tungsten carbide plate and the calculator predicted that the thrust plate would shatter, which it promptly did.
Any further information gladly accepted - it's been a long, long time since engineering school and what you don't use you lose, hence my reliance on on-line resources such as the site referenced above.
Failure of the ball seems relatively uncommon, I *think* it's only going to be a problem if the thrust plate material is as hard as the ball material. I was going to proceed on the assumption that the thrust plate would be softer than the ball (or ball end), thus the hardness of the ball isn't too important..
The calculator seems to give real world results - I know someone who design a table with a sapphire ball riding on a tungsten carbide plate and the calculator predicted that the thrust plate would shatter, which it promptly did.
Any further information gladly accepted - it's been a long, long time since engineering school and what you don't use you lose, hence my reliance on on-line resources such as the site referenced above.
If we knew how much mass the bearing was supporting, one could do a quick calculation of the amount of elastic distortion over the radius and whether it would approach E/20 (for a quick and dirty) for a "rigid" plate.
My belief is that it really isn't today or tomorrow that we should be worried about, but the cyclic damage from rotation. Think of a high cycle, high load, with small changes in the loading problem in fatigue. A softer plate material would relieve the bearing of some load, by the allowance of a greater contact area. (H = P/A) (P = load)
A simple calculation: 33 rpm * 60 min = 2000 revolutions. After only 50 hours, you're starting to approach 10^4 cycles. I put that in on a typical week. A typical year would start approaching 10^6 cycles, where the endurance limit is going to come into play. In that case, we want the overall stress to remain under the endurance limit, or roughly 30 ksi.
I'll try to simplify my formulas and post them either tonight or tomorrow (I have to grade some homeworks first), so that they can be used as a future reference. (emulating Mr. Kelly's work on this forum)
My belief is that it really isn't today or tomorrow that we should be worried about, but the cyclic damage from rotation. Think of a high cycle, high load, with small changes in the loading problem in fatigue. A softer plate material would relieve the bearing of some load, by the allowance of a greater contact area. (H = P/A) (P = load)
A simple calculation: 33 rpm * 60 min = 2000 revolutions. After only 50 hours, you're starting to approach 10^4 cycles. I put that in on a typical week. A typical year would start approaching 10^6 cycles, where the endurance limit is going to come into play. In that case, we want the overall stress to remain under the endurance limit, or roughly 30 ksi.
I'll try to simplify my formulas and post them either tonight or tomorrow (I have to grade some homeworks first), so that they can be used as a future reference. (emulating Mr. Kelly's work on this forum)
My knowledge of fatigue behaviour is fairly weak so what follows is me thinking out loud.
I thought the stress used in fatigue calculations was the cyclic stress not the total stress. Perhaps an example will make this clearer: if you have a member carrying a stress of say 100Mpa which varies by +/- 10Mpa every two seconds I thought that the stress used for the fatigue calculation would be the 20 MPa difference not the 110 Mpa peak.
If that is the case I can't see that fatigue stress is going to be a problem. I cannot see that the load on the thrust bearing varies very much, if it did it would create a lot of noise.
I thought the stress used in fatigue calculations was the cyclic stress not the total stress. Perhaps an example will make this clearer: if you have a member carrying a stress of say 100Mpa which varies by +/- 10Mpa every two seconds I thought that the stress used for the fatigue calculation would be the 20 MPa difference not the 110 Mpa peak.
If that is the case I can't see that fatigue stress is going to be a problem. I cannot see that the load on the thrust bearing varies very much, if it did it would create a lot of noise.
For a Wohler diagram (S-N) curve, the stress amplitude is used. However, the mean stress is used in conjunction (Goodman/Soderberg/Gerber diagram) with the cyclic amplitude to determine the maximum allowable number of cycles. If the bearing is near the yield stress, even small alternating stresses will cause fatigue.
I think this brings us back to Mr. Kelly's observation that it is best to use a thrust material with a lower modulus than that of steel. Delrin would be a good example. It is also important not to go overboard on the platter mass. A larger mass requires a larger bearing, which increases noise/rumble.
D
I think this brings us back to Mr. Kelly's observation that it is best to use a thrust material with a lower modulus than that of steel. Delrin would be a good example. It is also important not to go overboard on the platter mass. A larger mass requires a larger bearing, which increases noise/rumble.
D
I've run throught the calculations using a series of different materials from hardened steel to tin babbitt and a few polymers: Teflon, Delrin and Torlon.
It appears that D to the G was right, for any practical platter mass the contact pressure exceeds the elastic limit of every material except the hardened steel, so the analysis changes.
For practical purposes we can use the simplified version where the entire contact patch is in plastic flow so the ball will indent into the thrust pad until the contact area is large enough to support the platter mass.
I *think* we can just use the cross section of the ball as the maximal contact area and the yield stress of the material as the pressure limit, but I need to do some further reading.
It appears that D to the G was right, for any practical platter mass the contact pressure exceeds the elastic limit of every material except the hardened steel, so the analysis changes.
For practical purposes we can use the simplified version where the entire contact patch is in plastic flow so the ball will indent into the thrust pad until the contact area is large enough to support the platter mass.
I *think* we can just use the cross section of the ball as the maximal contact area and the yield stress of the material as the pressure limit, but I need to do some further reading.
Well, this thread is taking an interesting turn indeed.
It is all a bit beyond me, but I'm very curious to know what conclusion will emerge.
thank you very much for this interesting discussion.
MArco
It is all a bit beyond me, but I'm very curious to know what conclusion will emerge.
thank you very much for this interesting discussion.
MArco
Mark Kelly said:
Those are both pretty valid approximations. Using an extremely stiff material like sapphire will cause some elastic/plastic deformation in the bearing but would provide the smallest contact radius.
I guess I'm not sure what we're optimizing here?
ps. I work in contact mechanics, so I should be able to explain much better than this. Let me know what it is we'd like to accomplish and I can probably do a bit better.
Also, as far as platter materials go, I've heard nothing that comes close to delrin.
Update
I found time to work on my turntable again.
As I was never satisfied with the bearing (I cut up an old thorens for this project, which in the end proved quit worn) I decided to improve things.
For this I inserted a teflon sleeve in the bearing, with 4 defined contact points as in a well tempered turntable bearing. In this I put a Thorens sub platter with a 7.2 mm spindle from a TD160 MKII.
At first I tried this with a teflon thrust plate as well, but this didn't work. The teflon became dented too uch an the spindle started circling around the supposed centre point.
After removal of the teflon thrust plate things worked out quit well. The depression in the original thrust plate centres the spindle nicely. There is now very little platter run out (not more than with the original arrangement).
The new bearing arrangement is very quiet. The subplatter spins long without the belt attached.
The difference in wow and flutter can easily be heard on piano music with long sustained notes.
So definitely an improvement and it is very nice that a standard Thorens bearing can be easily upgraded to a well tempered look-a-like bearing.
MArco
I found time to work on my turntable again.
As I was never satisfied with the bearing (I cut up an old thorens for this project, which in the end proved quit worn) I decided to improve things.
For this I inserted a teflon sleeve in the bearing, with 4 defined contact points as in a well tempered turntable bearing. In this I put a Thorens sub platter with a 7.2 mm spindle from a TD160 MKII.
At first I tried this with a teflon thrust plate as well, but this didn't work. The teflon became dented too uch an the spindle started circling around the supposed centre point.
After removal of the teflon thrust plate things worked out quit well. The depression in the original thrust plate centres the spindle nicely. There is now very little platter run out (not more than with the original arrangement).
The new bearing arrangement is very quiet. The subplatter spins long without the belt attached.
The difference in wow and flutter can easily be heard on piano music with long sustained notes.
So definitely an improvement and it is very nice that a standard Thorens bearing can be easily upgraded to a well tempered look-a-like bearing.
MArco
Update: More scrap
I used to have my custom motor drive for the synchronous motor. It was a wien-bridge oscillator followed by a power amp and a step-up transformer.
Unfortunately this solution proved to be unstable. The wien-bridge oscillator deteriorated and the power supplied to the motor showed to much amplitude variation.
To solve things once and forever I dug up a Nintendo Gameboy Advance (gba) from the scrapyard. I've programmed it to play a 50 Hz sine which can be varied in frequency.
I'll substitute one of the buttons by a reed relais triggered by a small magnet on the platter to measure actual rpm. So the gba will be able to automagically adjust the frequency so that the platter spins at the desired rpm.
Unfortunately the gba outputs some hf distortion so I'll have to include a low pass filter to clean up the signal a bit. And while I'm at it I might use a phase -shifter and a second power amp and step up transformer to get rid off the phase-shifting cap at the motor.
to be continued ...
MArco
I used to have my custom motor drive for the synchronous motor. It was a wien-bridge oscillator followed by a power amp and a step-up transformer.
Unfortunately this solution proved to be unstable. The wien-bridge oscillator deteriorated and the power supplied to the motor showed to much amplitude variation.
To solve things once and forever I dug up a Nintendo Gameboy Advance (gba) from the scrapyard. I've programmed it to play a 50 Hz sine which can be varied in frequency.
I'll substitute one of the buttons by a reed relais triggered by a small magnet on the platter to measure actual rpm. So the gba will be able to automagically adjust the frequency so that the platter spins at the desired rpm.
Unfortunately the gba outputs some hf distortion so I'll have to include a low pass filter to clean up the signal a bit. And while I'm at it I might use a phase -shifter and a second power amp and step up transformer to get rid off the phase-shifting cap at the motor.
to be continued ...
MArco
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