Insane Hydraulics
Bold and audacious blog about fluid power
This is probably a dumb post, or at least it will feel like one to those of you with an engineering background, but I don't have an engineering background - so I feel I should make it anyway, and talk about the three "useless numbers" that were a mystery to me when I was a shop hand plucking bits of hydraulic knowledge from random catalogs.
Last week, when I was purging my home archives, I found an old hand-written note that read: "find explanation for: B10 life (bearings)... maximum corner power... mass moment of inertia..." It is quite interesting to be looking at your own handwriting and have no recollection of the circumstances you made the note in. Am I that old already? I reckon I was going through a hydraulic pump or motor catalog, and was taking notes of the terms I didn't know the meaning of.
Anyhow - let me provide the explanations (as a tribute to my younger self) and throw in a few interesting facts in the mix. Let us begin with the
I actually mentioned it before in my post on setting tapered bearings. In essence, - an L10 (or B10, which is the same thing) figure indicates a period after which ten percent of a large group of product samples will fail in given conditions. In other words - it is a statistics-based figure that allows you to estimate a product's life span. The key word is "estimate" - i.e. - roughly judge the value of. In real life, this figure is meaningless because the conditions a bearing will work in are unpredictable.
Just an example - look at the figures of Lh10 life for bearings of Danfoss series 51 bent-axis variable displacement motors (at 1500 rpm). And, by the way, the "h" in the "Lh10" supposedly stands for hours - I've heard an opinion that L10 for bearings can also be denoted in millions of revolutions, but I think I only encountered L10s in hours so far.
As you can see, with changes in the axis angle and/or the pressure differential, the L10 for the same motor can vary from 1400 to over 10000 hours, and since it is virtually impossible to predict the conditions a motor will face in a real-life application - these numbers are useless in practice. This is why many OEM catalogs omit mentioning the L10 life figures for the bearings altogether.
I've never had practical use for an L10 figure. I suppose it could be a consideration for some critical (maybe military) application - but I've never faced one.
Here's a peculiar quote from Rexroth: "...The service life of the axial piston unit is limited by the service life of the bearings fitted..." In my experience, average equipment users tend to drive their hydraulics into the ground way sooner the bearings get any chance to fail statistically, so... like I said - the L10 is a curious but useless number.
Now, let us move on to the
This is, by far, the coolest expression that can be applied to a hydraulic unit. The term "corner" comes from the fact that power can be described as a product of two variables, which in the case of a hydraulic motor (or pump) are the pressure and flow rate, and since there are physical limitations to the max flow rate and the max pressure, if you were to plot the operational range of a given unit on a two-axis PxQ chart, you would get a (often rectangular) shape, where the point with the highest possible hydrostatic power (max. flow rate times max. pressure) is located at a corner - hence maximum corner power.
Most hydrostatic transmissions I work on don't come even remotely close to the maximum corner power of its rotary components. So, in practical terms - at least for me - the maximum corner power is just a number in a catalog. But I must admit that it's always an impressive number! For example - a teeny tiny 60cc series 51 motor has the maximum corner power of a whooping 336 kW!
Finally, we got to the
I love this term! If you want to see a hydraulic tech scratch his head, all you need to do is show him a catalog of a hydraulic motor that he knows in and out because he's been working with it all of his life, open the page with the table with the specific data, and ask him what those "mass moment of inertia" figures mean.
MME essentially denotes how the mass of a rotating component is distributed in relation to the axis of rotation, and I, personally, don't like the term mass moment of inertia at all - I think the term rotational inertia is much more intuitive because it explains why you might ever want to know this number in the first place - i.e. - to determine how hard it is to change the rpm of a given rotary component.
Let me make it "super visual" for you. A rotating system with a 1 kg-meter-squared MME can be represented by a 1kg point mass rotating at a radius of one meter. Since our pumps and motors rarely have radiuses in the order of meters, I like to use decimeters (the length of your index finger) - and all you need for the conversion is to multiply kgm² by a hundred. For example - the 1 kgm² we just talked about is equal to 100 kgdm² - picture a mass of 100 kilograms rotating on an index-finger-long lever.
In practical terms - if you look at the data for the series 51 - you'll see that, for example, a 160cc motor has the MME of 0.0234 kgm². Now, it is pretty hard to imagine a 23 gram mass on a one meter long lever, but 2.3 kilograms on a 10cm-long lever make prefect intuitive sense (at least for me). Also - if you compare the MME of the Danfoss 160 with, say, the Rexroth A6VM160 - you will see that the Rexroth has the MME of 2.53 kgdm², which means A6VM is more inertial than the 51, and since their rotary groups are similar in diameter, we can estimate that the rotary group of the A6VM is a bit heavier.
Curious? Yes! But, once again - I've never ever seen a need to use this number in my practice, even in dynamic applications. Still, I like the fact that I have a general idea on what this (useless) number means.