Proper Spline Mesh

The standard practice for a non-sliding spline connection is to have the stripping strength of the spline equal to the shearing strength of the shaft. This condition would develop a maximum strength connection, assuming equal-strength materials for both the male and female splines. The design criteria for this condition to exist is that the length of engagement be equal to d^3/D^2. That's the cube of the spline root diameter divided by the square of the spline pitch diameter. The root diameter is always a little less than the pitch diameter so the length of engagement would wind up to be a little less than the pitch diameter. The pitch diameter is also a little less than the shaft diameter so the length of engagement would be somewhat less than the shaft diameter. How much less is determined by the actual relative diameters. For the sake of argument, assume that the pitch diameter is 95% of the shaft diameter and that the root diameter is 95% of the pitch diameter. That means that for equal strength (spline and shaft) the length of engagement should be about 80% of the main shaft outside diameter. [(0.95x0.95)^3]/[(0.95)^2)] = 0.81. A lesser engagement would mean the spline would strip first. A longer engagement would mean the shaft would shear first. Of course this is only applicable if the material strength is the same for both parts. If the coupling (female spline) is less strong that the shaft, then a longer engagement length is required to obtain the max strength of the joint. A spline that is subject to axial sliding during operation is quite different and the length of engagement is based on a maximum pressure on the side of the spline teeth and not the strength of the tooth itself.

Your 3/4" engagement with a 1-1/8" dia shaft is about 67% of the shaft dia. Unless you are going to push this equipment to the limits, I don't think you would have a problem with that. The means of failure would likely be stripping of the coupling rather than shearing of the shaft. That's probably a good thing, especially if the coupling is a little less strong than the shaft. That would mean the internal spline in the coupling would strip. I don't know the exact configuration of what you are talking about, but it is possible that replacing the coupling (if necessary) would be a lot more desirable than having to replace the shaft.

Rod