Are you guy's just not that into controls or trying to do meaningful work?

For those of you interested in Aric's recent breaking of a bunch of Aliens, I did some work to collect some data on the effective angle of each cam he tested.

Methodology:

I used the photos Aric scanned in of the cam lobes post-pulling, found here: http://www.shariconglobal.com/...cans/lobe_scans.html

Second, I ran these photos through the Dorrington software to obtain a theoretical center point. (found here: http://www.dorringtonclimbing.com

Third, I found the contact point for each lobe, using a combination of the photos Aric took of the cam placed in the jig, and the flat spot on the cam lobe. Wherever possible, I used the actual flat spot.

Fourth, I determined the effective cam angle in the jig for each lobe, and averaged them together. For each cam Aric put photos online, I used between two and four lobes. If the lobes were too bent, or if the results were identical across lobes, I did not use all four.

Lastly, I averaged these angles together to find the effective cam angle for each piece Aric tested.

The reasons these photos are more accurate to run through the Dorrington software are four-fold. First, because they are layed flat on a scanner, they are properly oriented to the "camera". Second, because the axle and nut are removed, leaving the axle hole in the same plane, the center of the stem cannot "appear" to be offset due to a slight change in camera angle. The center of the axle is exactly where it is. Third, the flat spot in the cam lobe shows exactly where the lobe contacted the fixture. This is much superior to the guesswork of looking at a photo of the cam in the fixture and trying to estimate where lobes that are hidden by the closer lobes are contacting the fixture. And lastly, in some cases, the different lobes were cammed quite different amounts. Looking at the cams after the fact made this obvious, and gave much more accurate readings on where the contact point is. I was then able to average the angles together.

With all that said, here is the raw data:

Code

Looks like within a cam size, there may be some correlation between angle and pullout force, such that the higher the angle, the lower the force. But I'm tired, and I haven't run the numbers.

Here are the pics:

http://s26.photobucket.com/...gles/?albumview=grid

GO

Gabe, have you been able to measure cam size? It will be difficult to control for the effect of cam size without such measurements. And without controlling for cam size, the analysis will be doomed.

Jay

What's the merit in reporting the average of the cam angles?

I am not much of a math person, but I believe you need 5 degrees of freedom to predict the actual cam angle of a log spiral with the axle off center (2 DOF to describe the cam, 2 DOF to describe where the axle is in relationship to the center of the spiral, and 1 DOF to describe how open the cam is).

Are you guy's just not that into controls or trying to do meaningful work?

Nope, I have not measured cam size. Frankly, I neither see the point nor do I know what measurement you're looking for, or how you think I could get it.

If you want to know the volume of material that needs to be moved before reaching the 35 degree slipping point, you would need to know more than just some dimension whatever that single dimension is you're looking for.

GO

According to Aric no other cams he's tested (and he's tested a bunch) fail by means of pulling from his jig.

GO

There is no significant relation between scanned angle and failure load (p-value=0.42) or percentage of rated strength (p-value=0.62), after adjusting for rated strength.

Edit: There is a significant negative correlation between post-test scanned angle and lobe hardness (r = -0.60, p-value = 0.01), suggesting that large post-test cam angles are the result of lobe softness. Post-test cam angle, therefore, probably isn't giving us much useful information.

Edit2: The (partial) correlation is even stronger (r = -0.70, p-value = 0.002), after controlling for rated strength.

Jay

As I recall, a blue Metolius TCU sheared out of the device.

Not even among cams of the same size? Oh well.


Could you explain what you mean here? You're saying that the effective cam angle - the angle between the walls of the jig and the axle at the moment before testing, predicts the lobe hardness? That doesn't make sense. Surely I'm misunderstanding you.

Edit2: The (partial) correlation is even stronger (r = -0.70, p-value = 0.002), after controlling for rated strength.

I'm saying that the observed post-test cam angle is probably primarily the consequence of the softness of the cam lobe. Softer lobes deform more.


Essentially, what this means is that, if you look at the correlation between scanned post-test angle and lobe hardness among cams of the same strength rating, the correlation is stronger than if you look at the correlation in the total sample. If that still doesn't make sense, let me know, and I'll give it another shot tomorrow, before I've drunk a half bottle or red wine (for the health benefits, of course).

Jay

So the theory is that if the cam starts with a higher angle, less force is required, because less metal has to be deformed.

Oh, so when you refer to the "post-test" angle, you're referring to the angles I measured from the leading edge of the flat spot. That was from another thread, nothing to do with this one. This measurement (also on images taken "post test") is of the estimated effective angles at the time of pulling.

GO

Gabe, I'm using the angle data from your first post in this thread. Are you saying that those numbers are estimates of the pre-test effective angles? If so, then (1) the explanation in your first post is unclear and misleading, and (2) I need to rethink the implications of my results.

Jay

Sorry if my OP was not clear. I've added the following to the OP to hopefully clarify exactly what I'm measuring:

The angle I'm measuring is the angle between the center of the axle and the point of contact between the edge of the fixture at the moment before Aric began pulling.

Hopefully this pic will clarify. Depicted is the right side cam lobe, the axle, and the right side of the fixture. The angle I'm measuring is the angle between the axle and the fixture at the moment before the cam starts getting pulled.



GO

Well, that makes the correlations I found difficult to interpret. Why would there be a strong (negative) correlation correlation between pre-test cam angle and lobe hardness? Are you confident that you can accurately measure pre-test cam angle from scans of post-test cam lobes? Elsewhere, another poster (forgot his username) asserted that the cam angle measured from post-test images will be biased because the test will have caused displacement of the cam center. That would (I think) explain this correlation, and I can't think of any other reasonable explanation.

Jay

Not quite... A pair of old U-stem camalots pulled from the fixture, but that was due to the divot in the lobes allowing the axles to flex further than they should have been able. And as Gunkie mentioned, the Blue TCU we tested while doing the Aliens also slipped from the fixture with a flattened lobe, but that occurred well above its rating. Most everything else I've done stayed put and broke in the fixture.

So, I think I have this straight: what you're trying to accomplish here is an examination of the relationship - if any - between initial effective cam angle and force at which the piece pulled.

My question is regarding step 2 of the process you outline. Why is the theoretical center point of the cam relevant if you're measuring instantaneous cam angle?

As I see it, attempting to do this with the images of cam-in-fixture, you need to find the centerpoint of the axle (this will be tough to do well with the off-center pictures) and (to do this well) use a bit of projective geometry to find the angle formed between the lobe contact point and the actual center of the axle... I don't see where the theoretical center of the spiral comes into play.

Not sure, but I think you're referring to a post in which someone mentioned that the cam angle would be changed by the bending of the axle, which is irrelevant to the angle I'm measuring which is the *starting* angle.

The axle holes of the softer lobes were deformed during the test, as their edges were compressed with the same forces as for the fixture side (less deformation though, because of the even contact surface with the axle). So far, you've been looking for a correlation between the hardness of the lobes and the failure cam angle, ignoring the translation of the center point toward the fixture, but the angle is further increased by the ovalization of the axle hole.

So let me get this straight, you're saying the higher the starting cam angle, the softer the lobes?

... I'm also not sure about your data. For example, two of the samples with the highest cam angles, (sample four and five, the two purple cams) had relatively hard lobes. And most of those with particularly hard lobes (9, 20, and 21) had average cam angles around 18 degrees.

And why would random error in my first set of data not obscure any real correlation in a more accurate set of data, while still having a good correlation to that more accurate set of data?

as measured from post-test images

Jay,

Could you please clarify which data is correlated with hardness? Or, specifically, what does


mean?

I'm confused as to which data sets you're using, and I'm only marginally clear on the data processing that Gabe's done... you seem to have a better handle on what data's out there and what it means - I'd appreciate it if you could clarify.

Thanks!

Gabe, can you clarify how the angles in the link in the preceding paragraph were obtained?

Jay

Yeah, I took the range of angles from Aric's report, (in which some of the cams were slightly tilted, enough to create a few degrees of skew), estimated the point of contact based on the photo (in which, typically, only one lobe could be seen well) and put those two together.

GO

At the moment the puller is out of commission while I resurface the fixture yet again, but it should be back together by the end of the week. The new texture will be a milled diamond knurl ~0.020" deep @ 20 tpi (to put 0.005" flats at the top of the knurls to help with wear), which will be approximately the max allowable roughness in the UIAA spec. I'm going to do the other side of the plates to something like ~0.010" since the actually cutting of the texture is quick and easy once the PITA of modifying the milling machine to do them is taken care of.

Starting to get caught up with this after taking a couple days (mostly) away from it... I'm rather annoyed with myself over this, as I had a steel ruler actually on the scanner bed while doing these but it was out of the cropped frame. Dammit! FWIW I did include the axles in the original scans and for all but the Blue and Black they're nominal 0.250" diameter. Scaling off that would be a bit of a pain, but not too bad.

Well, some of the cams appear to be pulling from the fixture when they flatten enough to create a 35 degree angle at the leading edge of the flat point. So the theory is that if the cam starts with a higher angle, less force is required, because less metal has to be deformed.

Sorry, could you try that again in plain English? Or else just tell me what you see wrong with the methodology I actually used.

Thanks,

GO

It appears you have attempted to measure the distance between centers (log spiral and axle) in previous posts (d= sqrt(x^2+y^2) and this distance may be represented by the black circles superimposed on the lines in figure 2. One can see that depending on whether the quantities y/r and x/r are positive or negative the range of the effective cam angle varies.

If one attempts to measure the cam angle of such a cam as it is expanded, one would expect to find a range of values. Taking the arithmetic mean of that data set would reflect the cam angle at only one point, which may not correspond to any of the points where the measurement was taken.

By averaging the different values you are eliminating information and not gaining anything in return.

The angle I'm measuring is the angle between the center of the axle and the point of contact between the edge of the fixture at the moment before Aric began pulling.
<snip>
The angle I'm measuring is the angle between the axle and the fixture at the moment before the cam starts getting pulled.
<snip>
Third, I found the contact point for each lobe, using a combination of the photos Aric took of the cam placed in the jig, and the flat spot on the cam lobe. Wherever possible, I used the actual flat spot.

Fourth, I determined the effective cam angle in the jig for each lobe, and averaged them together. For each cam Aric put photos online, I used between two and four lobes. If the lobes were too bent, or if the results were identical across lobes, I did not use all four.

Lastly, I averaged these angles together to find the effective cam angle for each piece Aric tested.

I would suggest therefore reporting the range of values measured and not the mean.

I suspect that the only case when taking the mean would be justified would be when the error in your measurement of the effective cam angle is on the same order as the range of possible effective cam angles. However, in such a case the cam might as well be constant angle because you cannot measure otherwise.

If you have a cam and the axle is not located at the center of the log spiral measuring it at one location (or averaging a bunch of positions, see previous post) will not provide any information other than the effective cam angle at that position. Five parameters need to be specified to predict the effective can angle of such a cam.

Can you measure a cam angle to a tenth of a degree? An estimate of error in these measurements would probably be helpful. What I mean is the value 14.5 (+/-0.2) DEG or 14.5 (+/-2) DEG?