Various observations and questions on the foregoing in more-or-less chronological order:
Thundersalt -- Nice to have empirical evidence that F=ma on the salt as well as on paper. Also nice solution.
Single diagonal vs. “X” vs. wishbone:
Both the single diagonal and wishbone would put the lateral location loads into one ball joint while the “X” could, possibly, with much precision and/or shimming, spread it over two. While under power, the forward tractive loads would tend to reduce the tensile side of the bending stress on the ball joint shank for single and X, but the wishbone would not benefit from carrying those loads. Under braking or trailing throttle this benefit becomes detrimental. Neither single diagonal nor wishbone act in anti-roll (except to the degree that they twist the axle and chassis, or deflect the bars longitudinally), while X is a fixed and probably high rate anti-roll device and consequently resists driveline torque. “X” largely precludes adjusting the static vertical load distribution on the tire contact patches via either the 4-bar links or springs. Depending on geometry used, single diagonal and wishbone, via the associated 4-bar linkages may have mild roll-steer effects. X would have minimal, since it is basically a trailing arm suspension with relative roll displacement limited by the stiffness of the lower X frame and springs.
Watt’s on top:
While such an arrangement would provide lateral location, with any vertical axle travel or chassis roll it is no longer a planar mechanism and would begin to impart small or moderate vertical loads into the system. Center pivot bearing would need thrust capability. High rear axle roll center.
Rick Byrnes “Watt’s” linkage:
This is an interesting arrangement, but the area of the two odd-shaped levers in the center is a bit of a mystery. Something in there must either have a sloppy fit, be riding in a slightly slotted out channel, have somewhat “compliant” pivot bearings, or be such that the vertical axle travel is quite restricted.
Also, the slight discontinuity at the chassis centerline in the horizontal tube to which the two links attach, is, or I assume, will be, welded as a single piece. Is this so?
Rick, for our edification, would you care to elaborate?
“Blue’s” reported set-up difficulties:
This seems odd, since with the X frame about the only thing that can be adjusted is the rear axle steer direction. It could be that moving the forward pivot points up or down to alternate locations, the side to side weight distribution was changed due to mis-matched pivot plate holes. Also, adjusting the upper links to different lengths would cause them to fight the lower X frame’s anti-roll resistance, probably resulting in erratic results.
Further to the statement “there are NO bending loads in a 4-link”: It is true that essentially no bending loads occur in a classic, unfettered, 4-bar linkage. However, when two of them are connected as in the X frame being discussed, the situation is entirely different. The roll resistance is provided primarily by the bending resistance of the cantilevered beam of the X members’ aft extension, and these vertical loads are carried as bending stress at the four ball joint shanks (due to the distance from the jam nut to the ball center). Lateral location loads are also seen as bending in the shanks, except that they are in the horizontal plane. These may be imposed on one forward joint and one rear joint, or somewhat shared between the two forward and two rear joints depending on the accuracy of the fitment and the stiffness of the bracketry.
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Just for fun, the following simple finite element model of the linkage was made in an effort to illustrate and quantify the kinds of load and stress distributions that can occur in the arrangement. Estimating plausible dimensions from Rob’s sketch, the model is 24” wide, 23” long from ball centerline to centerline, lower X frame 6” off the ground and the upper links 8” above the lowers. The tubulars are 1.25 OD x .125” wall, and the 3/4 inch “Heim” joints are modeled as 5/8” diameter stubs extending 1.5” from the ends of the tubulars. The forward pivot points are at fixed locations in space, e.g., on the chassis. The rear pivots are located on an artificially modeled “axle” (which is deleted from the diagrams for clarity in viewing the linkage.) Each part of the model consists of a numbered “element” which can be used to correlate the tabulated stress results to the location of the element in the model. A laterally acting (left-to-right) load of 1000 pounds was applied at ground level below the rear pivots, simulating sliding sideways on the salt with enough friction coefficient to generate that load. No driving or braking loads were included.
The tabulated stress results are maximum VonMises stress occurring in an element, and can be compared to the material strength properties. This maximum stress reported for the element occurs somewhere in that element, but is not necessarily uniform throughout the element. In most cases the maximum occurs at one end of the element with lesser values elsewhere in it. As this is not a detailed model, it is not conservative in that the effects of geometrical non-uniformities and resulting “stress concentrations” at junctions between the elements are not taken into account--things could easily be worse than depicted at the tubular joints, although the Heim stubs are probably well represented except for thread root stress concentrations.
Two sets of stresses are given, the first with both of the X frame forward joints restrained from lateral movement, and the second where the left-side joint can slide sideways as it may wish, passing the load to the right side joint.
As can be seen, even with this fairly innocuous loading, significant stress can be generated, amounting to a considerable portion of the likely material strength.
VM max (psi) VM max (psi)
Element No. Both joints fixed Only Rt. side fixed
1 36,546 17,668
2 39,743 41,449
3 663 667
4 663 667
5 38,340 67,226
6 31,598 29,990
7 663 667
8 663 667
9 10,932 10,582
10 460 463
11 10,329 11,124
12 460 463
13 10,955 11,756
14 22,099 22,119
15 23,166 23,176
16 27,155 27,042
17 28,195 28,241
