C-rig-Specific Phenomenon

Discovery of Shear Pulse

For yD ≠ 0, the projected location of the leading drive-axle will be forced by the roadway pavement to travel a longer distance than the trailing drive-axle during the same interval of time tD.  While the trailing drive-axle is traveling xD = S, the leading drive-axle is traveling 2Rθ as shown in the sketch.  The theoretical difference in circumferential distance traveled by the two drive axles is given by δ = 2Rθ - S, where δ ≡ shear pulse. 

The expression shear pulse is an in situ coinage for Unsprung Secrets.

The graph above indicates that for a change in roadway slope of about 15%, the shear pulse approaches a quarter of an inch of scuffing action on the pavement surface.  For undamaged roadway, however, one would expect a much smaller shear pulse, such that the tire would not actually scrub the pavement surface but only deform elastically.  Meanwhile...

The sketch below shows details about Drive Shaft #2, giving emphasis to the reality that instantaneous angular displacement φ is identical for the tandem drive-axles on a C-rig.


The tandem drive-axles are unsprung, thus vertically independent of one another.  Best keep in mind, however, Drive Shaft #2 has absolute angular authority over the two drive-axles.  Think steel-on-steel. The drive-train design in a C-rig tractor assures equivalence in angular displacement φ for all values of φ.

That absolute angular authority is maintained at any speed of the truck vX. 

By the way, the shear pulse phenomenon is independent of tractive effort.  Any damage from δ ≠ 0 can occur even if the C-rig is coasting with its transmission in neutral.

Sophisticated solvers know that the so-called differential on a roadway vehicle enforces mechanical averaging of angular rotations between its left DW and its right DW, which enables the vehicle to negotiating turns and roadway curves without scuffing action.

Roadway geometry balances the operation, such that the outside DW rotates through an angle φ + ∆φ while the inside DW rotates through an angle φ - ∆φ.  The average 'computed' by the differential will be [(φ + ∆φ) + (φ - ∆φ)]/2 = φ.

Vertical roadway deflections will not always be so polite. 

Let us suppose that a B-rig with its single drive-axle encounters a vertical deflection on the left-hand side of the roadway, which causes the left DW to rotate through an angle φ + ∆φ while the right DW continues to rotate through angle φ.  The average 'computed' by the differential would be given by [(φ + ∆φ) + φ]/2 = φ + ∆φ/2.  If the B-rig continues with no change in speed, the prime-mover must merely accommodate a minor change in torque corresponding to half of the incremental angular displacement imposed by the vertical deflection in the roadway.

Let us now suppose that a C-rig with its tandem drive-axles encounters a vertical deflection on the left-hand side of the roadway.  The left DW on the leading axle must rotate through an angle φ + ∆φ while the right DW on the leading axle continues to rotate through angle φ.  The average 'computed' by the differential on the leading axle would be given by [(φ + ∆φ) + (φ)]/2 = φ + ∆φ/2.  That will not be possible.  Here's why...

Since the trailing axle has not yet reached the deflection in the roadway, both of its DWs are rotating through angle φ.  The average 'computed' by the differential on the trailing axle would be (φ + φ)/2 = φ.  But, golly, the two differentials are lashed together steel-on-steel by Drive-Shaft #2, and φ + ∆φ/2 ≠ φ.

The conflict between the two differentials has nothing to do with the prime-mover.   The scuffing action will most likely occur under the left DW on the leading axle, as it is being bullied by the other three drive wheels.  Then farther along, when the vertical deflection comes under trailing axle, the scuffing action will take place under the left trailing DW.

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At this point we have ascertained that the drive-train design for the C-rig is over-constrained...

• Simultaneous Circumferential Distance: No difference can be allowed among the tandem drive-wheels (δ = 0), despite any discrepancies in the roadway profiles, AND...
  
• Instantaneous Angular Displacement: The value of φ is at all times identical for the tandem drive-axles, as constrained by Drive Shaft #2

...so something's gotta give.

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In a roadway hump, we see spatial forces of compression ('squeezing') in the pavement between the contact patches, increasing in the "Transient Zone" on the left and then decreasing in the "Transient Zone" ('stretching') on the right. 

The C-rig-specific phenomenon will have the same magnitude for a roadway dip.  Here's irony for you: The pavement would be experiencing spatial forces in compression between the contact patches -- same as for a hump.  Go figure. 

During the "Steady State Zone" of that particular roadway hump, both drive-axles, which are unsprung features of the drive train, are moving vertically along a constant radius of curvature R, first concave upward then inflecting to concave downward, all the while the pavement suffers constant longitudinal forces in compression from the C-rig's shear pulse δ. 

Think of drive-wheel tires on a C-rig as having 'analog memory', capable of storing the value of a shear pulse in one sense (squeezing) until it is 'erased' by a shear pulse in the opposite sense (stretching).  The technical term is elastic hysteresis.  Thus the most pronounced adverse effects attributable to shear pulse may be the accumulation of heat in the treads on drive-wheels, raising temperatures, and increasing wear -- all with no benefit for the transportation of the truck's payload.

In the absence of empirical evidence to support the various hypotheses set forth above, let us offer the solution to the Unsprung Secrets puzzle in the form of a proposed explanation...

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