Well, I did some very basic calculations to determine the shear force applied to the dog-teeth of the old design. I assumed 550 Nm of torque (worst-case) at my flywheel, which is 100 Nm higher than that recorded at the wheels during the recent dyno session. Following the torque path through the gearbox this results in (assuming zero frictional losses) an output torque of 1100 Nm, 856 Nm, 678 Nm, 550 Nm and 444 Nm in 1st though 5th gears respectively. Given that there are twelve dog-teeth that engage with each selector ring, given that I know the mean radius (to the centre-line through the teeth) of each dog ring, and given that I know the area of the root of each tooth, I then determined a shear stress of 42 MPa, 33 Mpa, 30 Mpa, 24 Mpa and 32 Mpa on the 1st through 5th dog-teeth respectively. Note that the 5th gear value is greater than, not less than, that of 4th gear since the 5th dog ring is located on the lay-shaft, not the output shaft like the other dog-rings.
Now, these values are calculated assuming a torque of 550 Nm applied (by the engine) to the spigot (input) shaft of the gearbox. In reality we can expect values up to three times higher than this due to the backlash between the selector-ring and the dog-ring. With that said, that still only gets us to a peak shear stress (on the 1st dog ring) of around 120 MPa. As a rule of thumb, the shear strength of a material is around half its tensile strength. Ordinary mild steel, for example, has a shear strength of around 150 MPa. So, given that my dog-rings were manufactured from case-hardened carbon-steel, why did my 3rd dog-ring fracture and fail? The answer is quite simple: Stress lines concentrate on sharp corners. Even though the mean (average) dynamic stress (over the area of the tooth) may not have exceeded 120 Mpa (as estimated for the 1st dog ring above) the stress at these concentrated points can be many times greater. I would estimate the shear strength of my dog-rings to be around 300 to 400 MPa, a figure easily exceeded given that I failed to radius these edges as Gareth recommended I do. An examination of the broken dog-ring shows quite clearly that the fractures formed at the sharp corners where the stress would have been at its greatest. When my third gear started to seize on the shaft it was the straw that broke the camels back and the 3rd dog-ring simply came apart.
My new design thus includes:
1) A proper bearing on the output shaft under the 3rd gear (same as the others), and
2) A proper radius at the root of each dog-tooth.
Sorry I didn't take your recomendation more seriously at that time Gareth. Until I had done my own analysis of the problem (and consulted with Dr Govender) I was really in no place to comment.
See
here for the new dog-ring design. Given that the new rings are larger than the old ones I have the room to include a decent radius at the base of the teeth.
Opinions and comments, as always, most welcome please.