BillyShope
Automotive
- Sep 5, 2003
- 263
This will interest only a few of you and most of those will file it in their "If anybody ever asks" folder, but I have the setup equation for the asymmetric 2link rear suspension, for a live axle, that I mentioned in another thread and I thought I'd share it. This would be an "arm," solidly attached to the axle and probably on the right side, and a "link," with bushings at each end, on the left. There would be, of course, a Panhard bar to locate the axle, though, I suppose, the link might be triangulated to serve that purpose.
The pivot for the arm would lie on the no squat/no rise line, as based on the CG height of the sprung mass. The link would be in a plane parallel to the XZ plane and would point toward a line which is parallel to the Y axis and which passes through the arm's rotation point on the no squat/no rise line.
The equation to follow will provide equal rear tire loading during acceleration and no squat or rise.
This can be considered a special case of the asymmetric 3link suspension first used by Jaguar on the early C-type. A solution would be found, then, in the equation I supplied for the student workbook which accompanies the Millikens' Race Car Vehicle Dynamics (bottom of page 204). (Note, when using this equation, that it's an "Rsubl" in the numerator of the second term and not the product of "R" and "l.") Unfortunately, I did not take unsprung mass into account in the derivation of that equation. The following, then, constitutes an improvement on my earlier equation and you might wish to add it to your book, if you have a copy. If you do, you will need to multiply the second term by the "K" defined in the book.
tangent of the link angle = (Mh + mr)/(Ml) - R(M + m)/(yGM)
where "M" is the sprung mass, "m" the unsprung, "h" the height of the sprung mass, "r" the height of the unsprung, "l" the wheelbase, "R" the rear tire loaded radius, "G" the axle ratio, "y" the offset of the arm from the centerline of the car, and the angle is measured positive upward from the horizontal at the rear mounting point. In most cases, the equation will yield a negative number. It is assumed that the sprung and unsprung CG's are on the car's centerline.
It's interesting to note that the lateral location of the link "disappears" during the derivation.
I would consider this an improvement over the 4link commonly used in drag race applications, both in its ability to achieve equal tire loading and in its simplicity, though it might be argued that the 4link's redundancy offers some safety benefits in case of a component failure.
But, it would be difficult to persuade a fabricator to switch from the 4link unless the superiority of another configuration could be proven. But, with all the parameters involved, small improvements are difficult to measure. I have, however, come up with a simple means to isolate these effects, which I intend to disclose in another thread for your comments.
The pivot for the arm would lie on the no squat/no rise line, as based on the CG height of the sprung mass. The link would be in a plane parallel to the XZ plane and would point toward a line which is parallel to the Y axis and which passes through the arm's rotation point on the no squat/no rise line.
The equation to follow will provide equal rear tire loading during acceleration and no squat or rise.
This can be considered a special case of the asymmetric 3link suspension first used by Jaguar on the early C-type. A solution would be found, then, in the equation I supplied for the student workbook which accompanies the Millikens' Race Car Vehicle Dynamics (bottom of page 204). (Note, when using this equation, that it's an "Rsubl" in the numerator of the second term and not the product of "R" and "l.") Unfortunately, I did not take unsprung mass into account in the derivation of that equation. The following, then, constitutes an improvement on my earlier equation and you might wish to add it to your book, if you have a copy. If you do, you will need to multiply the second term by the "K" defined in the book.
tangent of the link angle = (Mh + mr)/(Ml) - R(M + m)/(yGM)
where "M" is the sprung mass, "m" the unsprung, "h" the height of the sprung mass, "r" the height of the unsprung, "l" the wheelbase, "R" the rear tire loaded radius, "G" the axle ratio, "y" the offset of the arm from the centerline of the car, and the angle is measured positive upward from the horizontal at the rear mounting point. In most cases, the equation will yield a negative number. It is assumed that the sprung and unsprung CG's are on the car's centerline.
It's interesting to note that the lateral location of the link "disappears" during the derivation.
I would consider this an improvement over the 4link commonly used in drag race applications, both in its ability to achieve equal tire loading and in its simplicity, though it might be argued that the 4link's redundancy offers some safety benefits in case of a component failure.
But, it would be difficult to persuade a fabricator to switch from the 4link unless the superiority of another configuration could be proven. But, with all the parameters involved, small improvements are difficult to measure. I have, however, come up with a simple means to isolate these effects, which I intend to disclose in another thread for your comments.