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    The T-ech Rex fantic238's Avatar
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    Aug 2010
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    Understanding splined shafts and involute spline design basic theory.

    When it comes to axle swaps we always hear people saying "take this axle instead of that, it has "n" splines more and is tougher..." well, today we’re going to find out what is true about this statement and what does really count in the choice of a splined axle shaft.

    The progress in automotive technology has brought the manufacturing industry to optimize the fabrication of transmission organs to satisfy the more growing rotational speeds, torque delivery and balancing of rotating shafts. Conventional keyed shaft couplings don’t meet these requests anymore and have been consequently substituted by splined shaft couplings.

    The advantage of splines is to have a radial torque distribution and an auto-centering dynamics that still allows a semi-floating coupling and (in some cases) an axial slip or a full-floating coupling. These properties will have to be satisfied through all the range of torque and speed variations the shaft will encounter in its durable operating time.

    Another non less important aspect of a splined shaft is machining costs: we all know very well that the design of a serial component in automotive industry is firmly bound to its production costs. This cost is not particularly related to the forging-tooling techniques itself, but rather to the accuracy of the machineing, in one word: tolerances.

    Now keeping in mind all these leading aspects of a mechanical component we’ll do an overview of the different solutions that are offered on the market and most important, how do these different solutions affect our choice of a splined shaft for our beloved 4x4 rigs.

    Before we go deep into spline design, we will focus on the mayor issue for us four wheelers when it comes to axle shaft abuse: failure.
    Whoever has had the awful experience of snapping an axle (dana 35ers) will never forget that penetrating sound of the instantaneous breaking of a CrMo hardened full steel shaft….. SNAP! And the even worse consciousness that the next few hours are going to be painful (c-clippers there will have a laugh) because you left that damn spare shaft at home…

    How was this possible? What exactly happened? Well the greater lever of the taller tires has taken the shafts torsional stress over the elastic limit and into the plastic area. Steel is a material that reacts in a very particular way to applied forces. Imagine to be Hulk and hold firmly one end of the shaft (stuck wheel) and start twisting the other end (engine power), at a first moment the shaft will warp and if you remove the force it will go back the way it was. If you continue to twist, at a certain point you will feel as if the opposition of the material to the applied strength relaxes and it warps easily using the same amount of strength. That is the plastic phase. Of course if you remove the force you will still have the spring effect but at the end the shaft will have a finished deformation. What happens if I go further? The plastic deformation comes to an end when the material can’t distribute the deformation along the whole length anymore and it chooses a section where to break with a procedure called “necking”. This is the most important thing for us, the necking will occur at the smallest diameter of the shaft, always.

    The diagram (sigma epsilon curve) shows steel strain ( abscissae) versus torsion strength (ordinates). The linear slope corresponds to the elastic phase of the deformation (O-A-B), we want our steel to stay there. The horizontal portion (B-C) is the plastic phase, it means that we are permanently deforming our shaft in there, but if we remove the force the deformation will recover the elastic part coming back through a parallel of the slope, and the distance between the old O point and the new will be the finished deformation after the solicitation. The third section (C-D-E) is the necking phase where the steel hardens a bit at first and then tears up and snaps in point E.

    What this means in terms of toughness is the following: the diameter of a splined axle shaft must be the most constant as possible. Not big, not small, not tapered… CONSTANT, if this isn’t possible the transition between a diameter and another must be as smooth as possible, using big rounds and chamfers. So how has this shaft to be? General rule is that the minor diameter of the splined section must be at least equal or bigger than the nominal diameter of the shaft. This kind of shaft will have a thicker section where the splines will be cut.

    This shaft above i have designed is a Z26 spline to 32mm keyed coupling and it shows clearly the larger section of the splines and the big chamfer and round at the base of the bearing bed.

    The problem is that the automotive industry wants to save that tooling process and manufacturers roll forge in lieu of cutting the larger splines, thus the use of, e.g. 32 splines (rolled) in place of 10 splines (cut). It is the actual shaft diameter that has the largest effect on shaft strength. An example; a Jeep 23 spline shaft has a slightly larger minor diameter than a GM 27 spline shaft.

    An example of cut splines with the minor diameter smaller than the shaft diameter. The weak point is at the beginning of the splines.

    This is a modern rolled forged spline shaft (amc 20). These can be recognized by the high number of small splines and from the extrusion of the material at the base of the splines. The rolling/forging process cannot ensure a perfect involute shape of the side, but the advantage of this technique is that the shaft can receive heat treatment after the splines have been realized, although this happens rarely.

    Another aspect is the cutting geometry. The bigger are the splines, the more the geometry of the cut must be respected. In order to obtain a perfect linear contact surface, the side of a spline tooth is not flat, it is curved. This curve is called involute and looks grossomodo like a spiral.

    involute curve. The Curve is generated by "unwinding" a chord from the pitch diameter (black circle) that is the starting point of the curve.

    As you can imagine, the tooling of such a geometry isn't something easy, so there are three standards depending on the diameter and the tooling process.

    The flat root, mayor diameter fit is for the small shafts in order to assure the centering by the outer diameter.
    The fillet root is the one that will auto center itself as soon as torque is applied, and requires a very accurate tooling, and can be cut while the shaft is turning.
    The flat root is the most diffused among the tooled splines, machined by milling or single point cutting.

    Here are some videos of the digfferent techniques.


    Single point cutting

    CNC fully automatic milling with shaft in rotation

    and finally the cheap spline rolling
    Last edited by fantic238; 10-08-2010 at 06:37 AM.

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