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Calculating "gearmesh" freqs for a "cycloid" gearbox?|
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Help! My plant is in the process of obtaining a piece of equipment w/a Sumitomo / SM Cyclo CHH-6275AD-377 gear reducer on it (the last is the ratio of 377:1). It's a double reduction "cycloid" or "concentric" gear reducer with a 13:1 1st stage ratio and 29:1 2nd stage ratio, with 26 disc lobes and 28 ring gear housing pins on the 1st stage; 29 & 30 on the 2nd. Is anyone familiar w/the formula(s) for calculating expected operating / "gearmesh" / fault frequencies for such an animal? This a new configuration for me--I had to stare at the little video on their website for awhile to get a feel for how motion/power is transmitted!
Thank you! |
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Tony,
I've done some analysis on Sumitomo cycloidal disc reducers and as I recall, 2 x running speed was dominant due to the eccentric bearing. I have some data from a failure. I'll look for some more specifics tomorrow. Danny |
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Danny--Thanks for the help! These are an interesting concept--hopefully an engineering-sound one. I can't help but think the the number of lobes or pins must have some mathematical relationship to at least some of the speeds...? Let me know what you find!
Tony |
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Tony,
The attachment has a spectrum from a SM Cyclo reducer that was replaced. I never got to see it, but it was "all tore up" as they say. The PeakVue spectrum showed harmonics of output speed and 2 x input speed with sidebands spaced at output speed and 2 x output speed (meaning they were both there, but the even numbered sidebands were higher). There was impacting at output speed and 2 x input speed in the PeakVue waveform. Before I started doing vibration analysis, I rebuilt many of these drives and they will put up with an amazing amount of abuse. I had one come into the shop with about 4 gallons of water and a pint of oil. (We always recommended no more than a 1:1 ratio of water to oil) The most common cause of failure I have experienced is wear or damage to the eccentric bearing. Since it has no outer race, it is directly exposed to any contaminants inside the drive and a special synthetic lube is required. As far as I know, there is no real gear mesh vibration on this type of reducer. I took a training class with a guy from Sumitomo who was supposed to do analysis on their parallel shaft reducers, but he doesn't do that anymore and didn't know anything about vibration analysis on the cyclo drives. He also told me that they didn't have anybody in their US manufacturing center that did. As I recall all the bearing information is in the operators manual. The eccentric bearing will make all the normal defect frequencies, but I don't know what they are. SKF makes them, but I think they are proprietary for Sumitomo. Good Luck, Danny smcyclo.doc (60 Kb, 38 downloads) |
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Cool! I talked to an engineer in Virginia who gave me all the bearing info--it seems like the "eccentric" bearing is just a standard "NJ" series, only mounted on the eccentric portion of the input shaft(s) (two for a 2-stage / double reduction box). What I still can't quite wrap my mind around is how they come up with a higher speed than the initial input shaft speed (that speed plus the speed of the output speed). It seems like there's a lot of parts to wear in this design--pins, rollers, etc. Is that the case, or does the "compression" vs. "shear" action (per their literature) of the cams/lobes minimize that?
Thanks! Tony |
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Tony,
As I recall, the eccentricity is in the bore of the bearing not the input shaft. I'm not sure what you are referring to about the higher speed although something like that does ring a bell in the depths of my mind. I'll let you know if I recall anything about that. Yes there are lots of parts but I have never experienced a high wear rate. They claimed in a training class that there was no sliding friction in these which after much discussion was revised to say that there is no sliding friction in the load bearing portion of the drive, ie the contact between the lobes and rollers. There is sliding friction between the rollers and pins. The distribution of the load over 45% of the disc gives this design a 500% shock load rating as opposed to 150% for helical and 200% for worm gearing. (These are all from memory and it has been about 15 years since I regularly worked with these.) I have seen a few broken pins on the ring gear and even fewer in the low speed pins that engage the output shaft with the cycloidal disc, but very few. The lobe design does have one drawback in that it is not truly a constant speed drive. There are slight speed drops and surges as the lobe rises and falls over the rollers or maybe due to the eccentricity. This was found to be the cause of a minute oscillation in the thickness of paint when this design was used in an automotive paint line. Danny |
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Interesting. I can see that oscillation being a significant issue in any process application requiring relatively true constant speed--as in your example. Don't see that in their literature!
Tony |
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I wrote this up a while ago. I can't find the article on my computers just now, but here is the reference.
author = {William C. Foiles}, title = {A Matrix Assembly Technique to Calculate Epicyclic Gear Frequencies}, booktitle = {Proceedings IFToMM: Fourth International Conference on Rotor Dynamics}, pages = {213-216}, year = 1994, editor = {Ronald L. Eshleman and Neville F. Rieger}, address = {Chicago, Illinois}, month = {September 7-9}, organization = {International Federation for the Theory of Mechanisms and Machines }, I also wrote a program to follow the algorithms in the paper - no waranty implied. The program is an old dos program, use arrow keys and not the mouse. The program works by breaking the gear into basic 3 element components and connecting them. Play with the program, no manual, no guaranteed results. Regards, Bill Bill.Foiles@bp.com |
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Bill,
If I understand it correctly, your program is for epicyclic or planetary gearing. A cycloidal disc reducer is different from planetary in that it has no real gears, but a cycloidal disc with pins and rollers and an eccentric bearing. http://www.smcyclo.com/products/cyclo-story.shtml Danny |
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This looks like it would have similar relationships if one assumes non-slip boundary conditions.
The input shaft and eccentric cam act like a planet orbiting a sun gear with the eccentric cam being the orbiting planet. It orbits about the eccentricity, sun pitch diameter. You know the orbiting angular velocity. The ring gear for the first stage is fixed and does not rotate, not unlike some epicyclical gears. Besides the wobbly nature of the mechanism it seems to be very similar. Output speed looks like the second planet spin. http://www.darali.com/page17.html starts a good explanation. Regards, Bill Bill.Foiles@bp.com |
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Posts About vibration/alignment/balance
Calculating "gearmesh" freqs for a "cycloid" gearbox?
