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Kevin,
I meant to post back Friday and show where the error in your model was, but the go home bug bit pretty hard and I left work a little early...
Anyway this is the post you left Friday afternoon:
"I had thought SL was most significant before, but simple example of why I had since reconsidered:
Isolate the spindle/kingpin/tire system. assume bicycle tire for simplicity. position kingpin vertical for fixed pivot (now tire is on an angle, in contact with ground below). For a given pure torque applied to the
wheel, spindle rotation is different/opposite for plus and minus scrub radiuses, independent of the '20mm' parameter you referenced.
The FBD does seem to suggest SL should be strong factor, mitigated by SR.
Played a little with suspension with fea ... came up with an offset single traction bar for solid rear 'stang ... eliminated torque reaction that unloaded one rear tire."
OK, lets take a closer look at the moments acting on the kingpin and I'll show you the one you missed.
Same scenario bicycle tire on wheel. Kingpin at some angle relative to the tire which we will call "KPI". Tire is vertical. We apply a torque through the halfshaft (which we will assume is perfectly horizontal for now) to the wheel. We will call this torque "T"
Also let us asume a Static Loaded Radius of the tire/wheel combo "R". At the ground the tire has a force acting in the longitudinal direction equal to T/R. This force acts at a distance of the scrub radius "SR" from the kingpin. This is basically what your post said and you came to the conclusion that (T/R)*SR was the torque acting about the kingpin. That is only one of the torques acting about the kingpin, the one that you missed is T sin KPI since the kingpin is not vertical and the tire is. So now we re-sum moments and find that:
T * sin KPI + T/R * SR = 0
Multiplying both sides by R we get:
T*R * sin KPI + T * SR = 0
Factoring out the T we get:
T * (R*sin KPI + SR) = 0
R sin KPI + SR is equal to the Spindle length if we use small angle approximations for sin KPI.
So the moment arm that torques about the kingpin use is the spindle length, not the scrub radius.
(If the kingpin were vertical the spindle length would equal the scrub radius and the torque about the kingpin would be proportional to the scrub radius because it happened to equal the spindle length)
-Joe
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