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, Tue, 19 Jun 2001 11:18:28
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Interlaced response to your questions:
:" T sin KPI " how is this a moment on the spindle about the KPI? I guess
:if hub bearings were seazed...
I too had initial doubts that the T sin KPI was a moment acting about the kingpin since there were wheel bearings. In the end, using a lot of simple math and first principles it does work out so. Start rotating the kingpin into strange and large inclinations and imagine what would happen. The moment is "free" and a component of it does act about the kingpin. If I have time I will post that proof later today, but since I was not sure myself we both made an Adams model of the system and have proven it experimentally. It works. I know that it a crappy proof and hope to post a better one later, but trust me on this it does work. I have done quite a bit of work on the topic of torque steer.
:" T * sin KPI + T/R * SR = 0 " why must the sum be zero ... no steering
:knuckle?
Yup. I solved for the torque acting about the kingpin that the steer arm must react. I was removing the steer arm. Another way to arrive at the same conclusion would be to include the steer arm, set that equation equal to zero and than solve for the torque the steer arm needed to react. In the end it is the same. I had, T * sin KPI + T/R * SR = 0 and to be more precise it should read, "T * sin KPI + T/R * SR = Tn" I admitt I took a shortcut, but you can see how the math is the same. Basically instead of setting my equation equal to zero I should have set it equal to the steer arm torque. I was doing that in my head, without writing it down.
:" R sin KPI + SR is equal to the Spindle length if we use small angle
:approximations for sin KPI. " no way, as I see it, for very small
:angles SL=SR, as you noted. Actual relation is SL=SR+RtanKPI
Dude, ever hear of small angle approximations? Where x Sin theta and x tan theta are both approximately equal to x tehta with theta in radians. sin 10 degrees is equal to 0.174, tan 10 degrees is equal to 0.176. Like I said i was using small angle approximations. SL=SR+RtanKPI is the correct relation, but the error is small when using normal values for KPI if you substitute SL for SR+Rtan KPI.
I don't know how you arrived at your conclusion of Tn=(T/R)cosKPI(SL) but I do not agree with it.
Do you have access to SAE papers? I can point you to some that may clear this up.
-Joe
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