tag:blogger.com,1999:blog-1564958057737541664.post859487455551484551..comments2014-07-24T07:10:01.421-07:00Comments on On Bicycles, and.... what else is there?: Metrigear Vector Pt 6: Forces and Bending (2)djconnelhttp://www.blogger.com/profile/01484858820878605035noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-1564958057737541664.post-64611626342691115252009-10-24T03:51:40.359-07:002009-10-24T03:51:40.359-07:00Interesting! Curiously, I initially thought the s...Interesting! Curiously, I initially thought the sensors would pick up total force, not a bending moment. Jim Pampodopolous, an MIT engineer who collaborated on Bicycling Science Third Edition, said it would be a bending moment and not a force measured by the sensors. That's consistent with two parallel strain gauges, oriented longitudinally, one at the center axis and one away from the center, measuring the difference in strain.<br /><br />But if they were instead configured to measure shear strain, which is a change in vertical position along the axis of the pedal, then you're right that the driving force would be force, not a force times distance.<br /><br />So I guess the question is then whether it's relatively easier and more reliable to measure bending or to measure shear distortion. It's a hollow tapered cyclinder, so I think one would need to run some real numbers (preferably FEA) to see if there's a strong enough shear signal without second-order contamination from bending stress, and vice-versa.<br /><br />My money's would be on the bending moment. I suppose I could <i>ask</i>, but it's more fun to guess.<br /><br />It's funny I'm so interested in this topic. It sort of gives me an excuse to exercise some basic physics on a topic (bicycles) which I really enjoy.djconnelhttp://www.blogger.com/profile/01484858820878605035noreply@blogger.comtag:blogger.com,1999:blog-1564958057737541664.post-7337687434119993852009-10-23T20:32:59.314-07:002009-10-23T20:32:59.314-07:00The link shows shear force and bending diagrams. ...The link shows shear force and bending diagrams. Note that unlike bending moment, shear force is not a function of displacement along the beam. I don't know how the measurements are oriented in the Metrigear design, but it is possible to arrange the sensors such that the electrical output is a function of shear force.Jim Meyerhttp://www.blogger.com/profile/08570639966758644342noreply@blogger.comtag:blogger.com,1999:blog-1564958057737541664.post-76132030510499992072009-10-23T14:22:25.480-07:002009-10-23T14:22:25.480-07:00Thanks! The bending moment is the cross-product o...Thanks! The bending moment is the cross-product of a position and a force, which my freshman physics brain calls a torque, but I guess "bending moment" would be more clearly differentiated from the twisting moment applied to the pedal body.<br /><br />I'm trying to wrap my head around <a href="http://www.roymech.co.uk/Useful_Tables/Beams/Shear_Bending.html" rel="nofollow">Jim's reference</a>, but I think what he's saying is Bernoulli's idealized cantilever fails to adequately describe a relatively short hollow tapered cylinder like a pedal spindle, at least within the 1.5% error budget, and that off-diagonal elements of the stiffness matrix are needed to really solve the problem (not just the scalar term used in the simple bending analysis). So maybe a second order calibration is needed.djconnelhttp://www.blogger.com/profile/01484858820878605035noreply@blogger.comtag:blogger.com,1999:blog-1564958057737541664.post-56832333168926428152009-10-23T13:07:16.305-07:002009-10-23T13:07:16.305-07:00This is a good article, and I agree with what you ...This is a good article, and I agree with what you are saying, but it would be more clear if you referred to the bending load on the pedal spindle as a "moment" rather than a "torque".Our Crewhttp://www.blogger.com/profile/03118552935022733472noreply@blogger.comtag:blogger.com,1999:blog-1564958057737541664.post-77753099780345939842009-10-23T08:12:57.318-07:002009-10-23T08:12:57.318-07:00http://www.roymech.co.uk/Useful_Tables/Beams/Shear...http://www.roymech.co.uk/Useful_Tables/Beams/Shear_Bending.htmlJim Meyerhttp://www.blogger.com/profile/08570639966758644342noreply@blogger.comtag:blogger.com,1999:blog-1564958057737541664.post-56635934636992772802009-10-22T19:51:24.698-07:002009-10-22T19:51:24.698-07:00Well, I suppose this shows a difference: my backgr...Well, I suppose this shows a difference: my background in mechanics is <a href="http://web.mit.edu/physics/" rel="nofollow">undergraduate physics</a> where all sensors are viewed as ideal, whereas your background is in actually making things that work :). But it seems the curvature is the only "observable" along the two axes perpendicular to the spindle (along the longitudinal axis you can measure strain directly).djconnelhttp://www.blogger.com/profile/01484858820878605035noreply@blogger.comtag:blogger.com,1999:blog-1564958057737541664.post-71300815725581671962009-10-22T15:30:19.849-07:002009-10-22T15:30:19.849-07:00Here is something to noodle on:
What if the sensor...Here is something to noodle on:<br />What if the sensors don't measure bending moment?Jim Meyerhttp://www.blogger.com/profile/08570639966758644342noreply@blogger.com